JEE Mathematics Ellipse MCQs Set B

Question:  If x cos α + y sin α = P is a tangent to the ellipse x²/a² + y²b² =1 then-

• a) a² cos2 α + b² sin² α = P²
• b) a² sin2 α + b² cos² α = P²
• c) Both
• d) None of these

Answer: a² cos2 α + b² sin² α = P²

Question: The equation of tangents to the ellipse 9x² + 16y² = 144 which pass through the point (2, 3) is

• a) y = 3 ; x + y = 5
• b) x + y = 2
• c) y = 3
• d) x – y = 3

Answer: y = 3 ; x + y = 5

Question: 

• a) Centre
• b) Focus
• c) End of the major axes
• d) End of minor axes

Answer: Centre

Question: Chords of an ellipse are drawn through the positive end of the minor axes. Then their mid point lies on -

• a) an ellipse
• b) a circle
• c) a parabola
• d) a hyperbola

Answer: an ellipse

Question: The line x = at² meets the ellipse x²/a² + y²/b² = 1 in the real points if -

• a) | t | ≤ 1
• b) | t | < 2
• c) | t | >1
• d) None of these

Answer: | t | ≤ 1

Question: The eccentric angles of the extremities of latus rectum of the ellipse x²/a² + y²/b² =1 is

• a) tan^-1(±ae/b)
• b) tan^-1(±be/a)
• c) tan^-1(±b/ae)
• d) None of these

Answer: tan^-1(±ae/b)

Question: The equation x² + 4y² + 2x + 16y + 13 = 0 represents a ellipse

• a)

  

• b) None of these
• c) whose eccentricity is √3
• d) Both

Answer:

Question:

• a) 2n²
• b) 2m²
• c) 2n
• d) 2m

Answer:  2n²

Question: Product of the perpendiculars from the foci upon any tangent to the ellipse x²/a²  +  y²/b²=1 is

• a) b²
• b) a
• c) b
• d) a²

Answer: b²

Question: The equation of the ellipse which passes through origin and has its foci at the points (1, 0) and (3, 0) is-

• a) 3x² + 4y² = 12x
• b) 3x² + y² = 12x
• c) 3x² + 4y² = x
• d) x² + 4y² = 12x

Answer: 3x² + 4y² = 12x

More Questions....................................

Question: A man running round a racecourse notes that the sum of the distance of two flag posts from him is always 10 meters and the distance between the flag posts is 8 meters. The area of the region encloses by his path is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:  The distance of a point on the ellipse x²/6 + y²/2 = 1 from the = 1 from the centre is 2. Then eccentric angle of the point is

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: The point of the intersection of the tangent at the two point on the ellipse x²/a² + y²/b² =1 whose eccentricity differ by a right angle lies on the ellipse is

• a) x²/a² + y²/b² =2
• b) x²/a² + y²/b² = -2
• c) x/a + y/b = 1
• d) None of these

Answer: x²/a² + y²/b² =2

Question: Find the equation of the ellipse whose eccentricity is 1/2, the focus is (–1, 1) and the directrix is x – y + 3 = 0.

• a) 7x² + 7y²+ 10x – 10y + 2xy + 7 = 0
• b) 7x² + 7y²– 10x + 10y + 2xy + 7 = 0
• c) 5x² + 7y²+ 10x – 12y + 2xy + 7 = 0
• d) x² + 5y²+ 10x + 10y + 2xy + 7 = 0

Answer: 7x² + 7y²+ 10x – 10y + 2xy + 7 = 0

Question: Find the equation of the ellipse whose axes are along the coordinate axes, vertices are (± 5,0) and foci at (± 4,0).

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Centre, length of the axes and eccentricity of the ellipse 2x²+3y²–4x–12y+13 = 0 are

• a) (1, 2) ; √2 ; 2/√3; 1/√ 3
• b) (2, 2) ; √3 ;2 / √3; 2/ √3
• c) Both
• d) None of these

Answer: (1, 2) ; √2 ; 2/√3; 1/√ 3

Question:  Find the equations of the tangents to the ellipse 4x² + 3y² = 5 which are inclined at an angle of 60^º to the axis of x.

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The radius of the circle passing through the foci of the ellipse x²/16  +  y²/9 = 1, and having its centre (0,3) is-

• a) 4
• b) 3
• c) 7/2
• d) None of these

Answer: 4

Question: The eccentricity of the ellipse represented by the equation 25x² + 16y² – 150 x – 175 = 0 is-

• a) 3/5
• b) None of these
• c) 2/5
• d) 4/5

Answer: 3/5

Question:

• a) 2
• b) 0
• c) 1
• d) infinite

Answer: 2

Question:

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: A point on the ellipse x²/16 + y²/9 = 1 at a distance equal to the mean of the lengths of the semi-major axis and semi-minor axis from the centre is

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

(1) e+1/e-1 (2) e-1/e+1

(3) 1+e/1-e (4) 1-e/1+e

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question: Consider an ellipse x²/a² + y²/b²= 1, centred at point O and having AB and CD as its major and minor axes respectively. If S₁ be one of the foci of the ellipse, radius of incircle of triangle OCS₁, be 1 unit and OS₁ = 6 units, then The area of ellipse is –

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Consider an ellipse x²/a² + y²/b²= 1, centred at point O and having AB and CD as its major and minor axes respectively. If S₁ be one of the foci of the ellipse, radius of incircle of triangle OCS₁, be 1 unit and OS₁ = 6 units, then

• a) 15 units
• b) 20 units
• c) 10 units
• d) 25 units

Answer: 15 units

Question: Consider an ellipse x²/a² + y²/b²= 1, centred at point O and having AB and CD as its major and minor axes respectively. If S₁ be one of the foci of the ellipse, radius of incircle of triangle OCS₁, be 1 unit and OS₁ = 6 units, then If S be the director circle of ellipse then the equation of director circle of S is –

• a) x² + y² =√ 48.5
• b) x² + y² = 97
• c) x² + y² = 48.5
• d) None of these

Answer: x² + y² =√ 48.5

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement 1 : Ellipse x²/25 + y²/16 = 1and hyperbola 12x² – 4y² = 27 intersect each other at right angle.
Statement 2 : Whenever focal conics intersect, they intersect each other orthogonally.

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True.
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Question:

Statement-1 : Locus of centre of a variable circle touching two circles (x – 1)² + (y – 2)² = 25 and (x – 2)² + (y – 1)² = 16 is an ellipse.
Statement-2 : If circle S₁ = 0 lies completely inside the circle S₂ = 0 then locus of centre of a variable circle S = 0 which touches both the circles is an ellipse

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.