Conic Section Test

Result

Conic Section Test - 6

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is

A
4x² - 4xy + y² - 8x + 4y + 4 = 0

B
4x² + 4xy + y² - 8x + 4y + 4 = 0

C
4x² + 5xy + y² + 8x - 4y + 4 = 0

D
4x² - 4xy + y² - 8x - 4y + 4 = 0
Question 2
4 / -1

If a point p moves such that is distances from the point A(1, 1) and the line x + y + 2 = 0 are equal, then the locus of P is

A
a straight line

B
a pair of straight lines

C
a parabola

D
an ellipse
Question 3
4 / -1

If the foci of an ellipse are (± √5, 0) and its eccentricity is √5/3, then the equation of the ellipse is

A
9x² + 4y² = 36

B
4x² + 9y² = 36

C
36x² + 9y² = 4

D
9x² + 36y² = 4

Solution
Question 4
4 / -1

A
a² + b²

B
(a + b)²/ 2

C
ab

D
(a - b)²/ 2
Question 5
4 / -1

If tangents are drawn to the ellipse x² + 2y² = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

A

B

C

D
Question 6
4 / -1

The point on the parabola y² = 64x which is nearest to the line 4x + 3y + 35 = 0 has coordinates

A
(9, -24)

B
(1, 81)

C
(4, - 16)

D
(-9, -24)
Question 7
4 / -1

A

B

C

D
Question 8
4 / -1

If the line x + y - 1 = 0 is a tangent to the parabola y² - y + x = 0, then the point of contact is

A
(0, 1)

B
(1, 0)

C
(0, -1)

D
(-1, 0)
Question 9
4 / -1

If the line x cos α + y sin α = p be normal to the ellipse

A
p² (a² cos² α + b² sin² α) = a² - b²

B
p² (a² cos² α + b² sin² α) = (a² - b²)²

C
p² (a² sec² α + b² cosec² α) = a² - b²

D
p² (a² sec² α + b² cosec² α) = (a² - b²)²
Question 10
4 / -1

The line 3x + 5y = 15√2 is a tangent to the ellipse

A
π/6

B
π/4

C
π/3

D
2π/3