Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q I

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Find the equation of the tangent and normal to the parabola $x^{2} - 4 x - 8 y + 12 = 0$ at $(4, \frac{3}{2})$

Important Questions on Parabola

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q I

Find the value of

k

if the line

2 y = 5 x + k

is a tangent to the parabola

y^{2} = 6 x

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q I

Find the equation of the normal to the parabola $y^{2} = 4 x$ which is parallel to $y - 2 x + 5 = 0 .$

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q I

Show that the line

2 x - y + 2 = 0

is a tangent to the parabola

y^{2} = 16 x

. Find the point of contact also.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q I

Find the equation of tangent to the parabola

y^{2} = 16 x

included at an angle

60 °

with its axis and also find the point of contact.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II

Find the equation of tangent to the parabola

y^{2} = 16 x

which are parallel and perpendicular respectively to the line

2 x - y + 5 = 0

, also find the coordinates of their points of contact.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II

If

l x + m y + n = 0

is a normal to the parabola

y^{2} = 4 a x

, then show that

a l^{3} + 2 a l m^{2} + n m^{2} = 0

.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II

Show that the equation of common tangent to the circle

x^{2} + y^{2} = 2 a^{2}

and the parabola

y^{2} = 8 a x

are

y = \pm (x + 2 a)

.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Mathematics Paper 2B>Chapter 3 - Parabola>Exercise 3(b)>Q II

Prove that tangents at the extremities of a focal chord of a parabola intersect at right angles on the directrix.