Conic Section Test

Result

Conic Section Test - 22

Score
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Weekly Quiz Competition

Question 1
4 / -1

If a normal chord at a point on the parabola y² = 4ax subtends a right angle at the vertex, then t equals

A
1

B
√2

C
2

D
√3
Question 2
4 / -1

The slopes of the focal chords of the parabola y² = 32x, which are tangents to the circle x² + y² = 4 are

A

B

C

D
Question 3
4 / -1

The two curves x³ - 3xy² + 2 = 0 and 3x²y - y³ - 2 = 0, is

A
touch each other

B
cut at an angle π/4

C
cut at an angle π/3

D
cut at an angle π/2
Question 4
4 / -1

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet a point lying y = 2x + a, a > 0.
length of chord PQ is

A
7a

B
5a

C
2a

D
3a
Question 5
4 / -1

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet a point lying y = 2x + a, a > 0.
If chord PQ students an angle θ at the vertex of y² = 4ax, then tan θ is equal to

A

B

C

D
Question 6
4 / -1

A circle, 2x² + 2y² = 5 and a parabola, y² = 4√5x.
Statement I An equation of a common tangent to these curve is y = x + √5.
Statement II If the line, y = mx + √5/m (m ≠ 0) is the common tangent, the m satisfies m⁴ - 3m² + 2 = 0.

A
Statement I is correct. Statement II is correct. Statement II is correct explanation for Statement I

B
Statement I is correct, Statement II is correct. Statement II is not a explanation for Statement II

C
Statement I is correct. Statement II is correct

D
Statement I is correct. Statement II is correct
Question 7
4 / -1

The line 2x + y + k = 0 is a normal to the parabola y² = -8x, if k is equal to

A
-24

B
12

C
24

D
-12
Question 8
4 / -1

A

B

C

D

Solution
Question 9
4 / -1

A
Statement I is correct, Statement II is correct

B
Statement I is correct, Statement II is correct; Statement II is a correct explanation for Statement I

C
statement I is correct, Statement II is correct, Statement II is not correct explanation for Statement I

D
Statement I is correct, Statement II is incorrect
Question 10
4 / -1

The values of m, for which the line y = mx + 2 is a tangent to the hyperbola 4x² - 9y² = 36 are

A

B

C

D