Conic Section Test

Result

Conic Section Test - 17

Score
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Rank
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Weekly Quiz Competition

Question 1
4 / -1

The circle x² + y² = a² intersects the hyperbola xy = c² in four points (x_i, y_i), for i = 1, 2, 3 and 4, then y₁ + y₂ + y₃ + y₄ equals

A
0

B
c

C
a

D
c⁴
Question 2
4 / -1

Consider the two curves C₁ : y² - 4x and C ₂ : x² + y² - 6x + 1 = 0, then

A
C₁ and C₂ touch each other at only one point

B
C₁ and C₂ touch each other at exactly two points

C
C₁ and C₂ intersect (but do not touch ) at exactly two points

D
C₁ and C₂ neither intersect nor touch each other
Question 3
4 / -1

A parabola is drawn with its focus at (3, 4) and vertex at the focus of the parabola y² - 12x - 4y + 4 = 0. The equation of the parabola is

A
y² - 8x - 6y + 25 = 0

B
y² - 6x + 8y - 25 = 0

C
x² - 6x - 8y + 25 = 0

D
x² + 6x - 8y - 25 = 0
Question 4
4 / -1

A

B

C

D
None of these
Question 5
4 / -1

x = 4 (1 + cos θ) and y = 3(1 + sinθ) are the parametric equations of

A

B

C

D
Question 6
4 / -1

The equation of the parabola whose focus i (3, -4) and directrix 6x - 7y + 5 = 0, is

A
(7x + 6y)² - 570x + 750y + 2100 = 0

B
(7x + 6y)² + 570x - 750y + 2100 = 0

C
(7x - 6y)² - 570x + 750y + 2100 = 0

D
(7x - 6y)² + 570x - 750y + 2100 = 0
Question 7
4 / -1

A
λ > 5

B
λ < 2

C
2 < λ < 5

D
2 > λ > 5
Question 8
4 / -1

The locus of the mid - point of the line joining focus and any point on the parabola y² = 4ax is a parabola with the equation of directrix as

A
x + a = 0

B
2x + a = 0

C
x = 0

D
x = a/2
Question 9
4 / -1

The two parabolas x² = 4y and y² = 4x meet in two distinct points. One of these is the origin and the other is

A
(2, 2)

B
(4, -4)

C
(4, 4)

D
(-2, 2)

Solution
Question 10
4 / -1

The equation of the ellipse having vertices at (± 5, 0) and foci (± 4, 0) is

A

B
9x² + 25y² = 225

C

D
4x² + 5y² = 20