Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 11

EASY

11th Odisha Board

IMPORTANT

Earn 100

Find the angle which a double ordinate of length $2 a$ of parabola $y^{2} = a x$ subtends at its vertex and focus.

Important Questions on Conic Sections

HARD

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Obtain the equations of the tangent and normal of the parabola

y^{2} = 4 a x

at a point where the ordinate is equal to three times the abscissa.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Find the equation of tangents and normals to the parabola

y^{2} = 4 a x

at the ends of its latus rectum.

HARD

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Find the equations of tangents and normals to the parabola

y^{2} = 4 a x

at the points where it is cut by the line

y = 3 x - a .

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Show that the tangent to the parabola

y^{2} = 4 a x

at the point

(a^{1}, b^{1})

is perpendicular to the tangent at the point

(\frac{a^{2}}{a^{1}}, \frac{- 4 a^{2}}{b^{1}}) .

HARD

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

A tangent to the parabola

y^{2} = 8 x

makes an angle

45 °

with the line

3 x - y + 5 = 0 .

Find the equation and the point of contact.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Prove that for all values of

k,

the line

y = k (x + a) + \frac{a}{k}

is a tangent to the parabola

y^{2} = 4 a (x + a)

.

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Obtain the condition that the line

l x + m y + n = 0

will touch the parabola

y^{2} = 4 a x .

MEDIUM

11th Odisha Board

IMPORTANT

Bureau's Higher Secondary Elements of Mathematics Vol.1>Chapter 12 - Conic Sections>EXERCISES 12 (b)>Q 12

Prove that the line

4 x - 2 y - 1 = 0

touches the parabola whose focus is at

(0, 0)

and directrix is the line

y = 2 x - 1 .