Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 47

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IMPORTANT

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Eccentricity of the conic $x^{2} - 4 x - 4 y + 4 = 0$ is

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Important Questions on Parabola

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 48

In the parabola

y^{2} = 4 a x,

the length of chord passing through the vertex and inclined to the axis at an angle of

\frac{π}{4}

is

HARD

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 49

Slope of the chord of parabola

y^{2} = 4 a x

which passes through the point

(- 6 a, 0)

and which subtends an angle of

45 °

at the vertex, is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 50

A line

y = \sqrt{3} x + λ

is drawn through focus

S

of the parabola

y^{2} = 8 x + 16

. If two intersection points of the given line and the parabola are

A

and

B

such that perpendicular bisector of

A B

intersects the

x

-axis at

P

then the length of

P S

is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 51

Let

C

be the locus of the mirror image of a point on the parabola

y^{2} = 4 x

with respect to the line

y = x

. Then the equation of tangent to

C

at

P (2, 1)

is :

HARD

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 52

An equilateral triangle is inscribed in the parabola

y^{2} = 8 x

with one of its vertices at the vertex of the parabola. Then, the length of its side is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 53

The length of the chord of the parabola

x^{2} = 4 y

having equation

x - \sqrt{2} y + 4 \sqrt{2} = 0

is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 54

If two of the normal of the parabola

y^{2} = 4 x

that passes through

(15, 12)

are

4 x + y = 72

and

3 x - y = 33

, then the third normal is

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IMPORTANT

Mathematics Crash Course KCET (UG)>Chapter 18 - Parabola>Exercise 1>Q 55

Length of the normal chord of parabola

y^{2} = 4 x

which makes an angle of

\frac{π}{4}

with the axis of

x

is