JEE Mathematics Parabola MCQs Set C

Question: The vertex of the parabola x² + 8x + 12y + 4 = 0 is:

• a) (– 4, 1)
• b) (– 4, –1)
• c) (4, –1)
• d) (4, 1)

Answer: (– 4, 1)

Question: The solution of dy/dx = ax+h/by+k represents a parabola when

• a) a = 0, b ≠0
• b) a = 1, b = 2
• c) a = 0, b = 0
• d) a = 2, b = 1

Answer: a = 0, b ≠0

Question: In a parabola semi-latus rectum is the harmonic mean of the:

• a) segment of a chord
• b) segment of focal chord
• c) segment of the directrix
• d) none of these

Answer: segment of a chord

Question: At what point on the parabola y² = 4x the normal makes  equal angles with the axes?

• a) (1, – 2)
• b) (9, 6)
• c) (4, 4)
• d) (4, – 4)

Answer: (1, – 2)

Question: If (2, 0) is the vertex and y-axis is the directrix of a parabola, then its focus is:

• a) (4, 0)
• b) (2, 0)
• c) (– 2, 0)
• d) (– 4, 0)

Answer: (4, 0)

Question: If m₁ and m₂ are the slopes of the tangent to the parabola x²/25 + y²/16 = 1, which passes through the point (6, 2), then the value of (m1 + m2) is

• a) 24/11
• b) 4/11
• c) 14/11
• d) 15/11

Answer: 24/11

Question: Common tangents to the parabola y = x² and y = – (x – 2)² are

(1) y = 4 (x – 1)   (2) y = 0
(3) y = –4 (x – 1) (4) y = –30x – 50

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

Answer: 1 and 2 are correct

Question: The tangent PT and the normal PN to the parabola y² = 4ax at a point P meet its axis at points T and N, respectively. The locus of the centroid of the triangle PTN is a parabola whose

(1) vertex = (2a/3, 0 (2) directrix, x = 0 (3) focus = (a, 0) (4) latus rectum = 2a/3

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

Answer: 1 and 3 are correct

Question: Three normals to the parabola y² = x can be drawn through a point (c, 0), if

(1) c = 3/4 (2) 0 < c < 1/2

(3) c > 1/2 (4) c = 1/2

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

Answer: 1 and 3 are correct

Question:

Statement-1 : If straight line x = 8 meets the parabola y² = 8x at P and Q then PQ subtends a right angle at the origin.
Statement-2 : Double ordinate equal to twice of latusrectum of a parabola subtends a right angle at the vertex.

• 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.

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

Question: 

Statement-1 : If point P (4, –2) is one end of focal chord PQ of y² = x then slope of tangent at Q is –1/4.
Statement-2 : Tangent at one end of focal chord is parallel to normal to other end.

• 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.

Question:

Statement-1 : Length of focal chord of a parabola y² = 8x making an angle of 60° with x-axis is 32.
Statement-2 : Length of focal chord of a parabola y² = 4ax making an angle α with x-axis is 4a cosec2 α.

• 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 NOT a correct explanation for Statement-1

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

Question: Let V be the vertex and L be the latus rectum of the parabola x² = 2y + 4x – 4. Then the equation of the parabola whose vertex is at V, latus rectum is L/2 and axis is perpendicular to the axis of the given parabola.

• a) y² = x – 2
• b) y² = 6 – x
• c) y² = x – 4
• d) y² = 4 – x

Answer: y² = x – 2

Question: The latus rectum of a parabola whose directrix is x + y – 2 = 0 and focus is (3, –4) is :

• a) 3 √2
• b) -3 √2
• c) -3 / √2
• d) none of these

Answer: 3 √2

Question: The locus of the poles of the focal chords of a parabola is the :

• a) directrix
• b) none of these
• c) axis
• d) tangent at the vertex

Answer: directrix

Question: The equation of parabola, whose vertex is (1, – 2) and focus (1, – 1) is :

• a) (x – 1)² = 4 (y + 2)
• b) (x + 1)² = 4 (y + 2)
• c) x² = 4 (y + 2)
• d) (x + 1)² = 4 (y – 2)

Answer: (x – 1)² = 4 (y + 2)

Question: The equation of the parabola with the axis on the y-axis and passing through origin and point (6, –3) is :

• a) x² = –12y
• b) y² = – 12x + 6
• c) x² = 12y
• d) y² = 12 x + 6

Answer: x² = –12y

Question: The equation of the line parallel to x-axis and passes through the vertex of the parabola 2x² + 5y – 3x + 4 = 0 is :

• a) x =3/4
• b) y =3/4
• c) y = -3/4
• d) x – 3y = 5

Answer: x =3/4

Question: The equation of the latus rectum of the parabola x² + 4x + 2y = 0 is

• a) 2y = 3
• b) 2y + 3 = 0
• c) 3y = 2
• d) 3y + 2 = 0

Answer: 2y = 3

Question:   Eccentricity of the parabola x² – 4x– 4y + 4 = 0 is equal to

• a) e = 1
• b) e = 4
• c) e = 0
• d) e > 4

Answer: e = 1

Question:  The line y = mx + 1 is a tangent to the parabola y² = 4x, if :

• a) m = 1
• b) m = 4
• c) m = 2
• d) m = 3

Answer: m = 1

Question: The directrix of the parabola x² – 4x – 8y + 12 = 0 is :

• a) y = –1
• b) y = 0
• c) x = 1
• d) x = –1

Answer: y = –1

Question: Two tangents are drawn from the point (– 2, –1) to the parabola y² = 4x. If a is the angle between these tangents, then tan a is equal to

• a) 3
• b) 2
• c) 1/3
• d) 1/2

Answer: 3

Question: The equation of the parabola whose vertex is at (0, 1) and the focus is at (0, 0) is

• a) x² + 4y – 4 = 0
• b) y² + 4 x – 4 = 0
• c) y² + 4x + 4y – 4 = 0
• d) None of these

Answer: x² + 4y – 4 = 0

Question:  The slope of tangents drawn from a point (4, 10) to the parabola y² = 9x are

• a) 1/4 , 9/4
• b) 1/4 , 3/4
• c) 1/4 , 3/3
• d) none of these

Answer: 1/4 , 9/4

Question: The focus of the parabola y² – 4y – 8x + 4 = 0 is:

• a) (2, 2)
• b) (2, 1)
• c) (1, 2)
• d) (1, 1)

Answer: (2, 2)

Question: If x = my + c is a normal to the parabola x² = 4ay, then value of c is:

• a) – 2am – am³
• b) 2am + am³
• c) none of these
• d) Both

Answer: – 2am – am³