Hyperbola Test

Result

Hyperbola Test - 4

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

Consider a branch of the hyperbola x² - 2y² - 2y - 6 = 0 with vertex at the point A. Let B be one of the end points of its latus rectum. If C is the focus of the hyperbola nearest to the point A, then the area of the triangle ABC is

A

B

C

D
Question 2
4 / -1

If α + β = 3π then the chord joining the points 'a' and 'b' for hyperbola passes through

A
focus

B
centre

C
one of end points of transverse axis

D
one of end points of conjugate axis

Solution

equation of the chord joining a andb is

it passes through (0, 0)
Question 3
4 / -1

The number of tangents and normals to the hyperbola of the slope 1 is

A
2, 2

B
2, 0

C
0, 0

D
0, 2

Solution

Equation of tangents and normal with slope 'm' will be
Question 4
4 / -1

From any point on the hyperbola tangents are drawn to the hyperbola The area cut off by the chord of contact on the asymptotes is equal to

A
ab/2

B
ab

C
2ab

D
4ab

Solution

Let (x₁ y₁) be point on
chord to

Area formed by the lines = 4ab
Question 5
4 / -1

If the line ax + by + c = 0 is a normal to the hyperbola x y = 1, then

A
a > 0, b < 0

B
a > 0, b > 0

C
a < 0, b < 0

D
none of these
Question 6
4 / -1

A tangent to the parabola x² = 4ay meets the hyperbola x² - y² = a² at two points P and Q, then midpoint of P and Q lies on the curve

A
y³ = x (y- a)

B
y³ = x² (y- a)

C
y² = x² (y- a)

D
y² = x³ (a- y)

Solution

Equation of tangent to parabola y = mx- am² .......(1) equation of chord of hyperbola whose midpoint is (h, k) is hx - ky = h² - k² ...... (2) form (1) and (2)
Question 7
4 / -1

The point of intersection of two tangents to the hyperbola x²/a² – y²/b² = 1, the product of whose slopes is c², lies on the curve.

A
y² – b² = c² (x² + a²)

B
y² + a² = c² (x² – b²)

C
y² + b² = c² (x² – a²)

D
y² – a² = c² (x² + b²)
Question 8
4 / -1

Let P(a secθ, b tanθ) and Q(a secφ, b tanφ) where θ+φ = π/2, be two points on the hyperbola If (h, k) is the point of the intersection of the normals at P and Q, then k is equal to

A

B

C

D

Solution

Equation of normal at P (θ) is
ax+bycosecθ = (a² +b²)secθ .......(1)
And at Q (φ) is
ax + bycoseφ = (a² +b²) secφ
⇒ ax +bysecθ = (a² +b²)cosecθ ......(2)
From (1) and (2)
Question 9
4 / -1

Foot of normals drawn from the point p(h,k) to the hyperbola will always lie on the conic

A

B

C

D

Solution

Equation of normal at any point (x₁, y₁) is it passes through
P (h, k) then thus (x₁, y₁) lie on the conic
Question 10
4 / -1

A variable chord PQ, x cos θ + y sin θ = P of the hyperbola subtends a right angle at the origin. This chord will always touch a circle whose radius is

A
a

B

C

D

Solution

Combined equation of lines joining the points of intersection of the chord with origin is

these lines are mutually perpendicular if

thus chord becomes x cos θ + y sin θ = which is clearly a tangent to the circle having centre at origin and radius is equal to