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

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Earn 100

The normal at a point $t_{1}$ on $y^{2} = 4 a x$ meets the parabola again in the point $t_{2}$ . Then prove that $t_{1} t_{2} + {t_{1}}^{2} + 2 = 0$

Important Questions on Parabola

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

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

From an external point

P

tangents are drawn to the parabola

y^{2} = 4 a x

and these tangents make angles

θ_{1}, θ_{2}

with its axis, such that

\cot θ_{1} + \cot θ_{2}

is a constant

' d'

. Then show that all such

P

lie on a horizontal line.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

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

Show that the common tangents to the circle

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

and the parabola

y^{2} = 4 a x

intersect at the focus of the parabola

y^{2} = - 4 a x

.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

The sum of the ordinates of two points on

y^{2} = 4 a x

is equal to the sum of the ordinates of two other points on the same curve. Show that the chord joining the first two points is parallel to the chord joining the other two points.

HARD

12th Andhra Pradesh Board

IMPORTANT

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

If a normal chord at point

' t'

on the parabola

y^{2} = 4 a x

subtends a right angle at vertex, then prove that

t = \pm \sqrt{2}

.