Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 54

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From point $P (8, t); t$ being the parameter, tangents are drawn to the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{12} = 1$ so as to touch the curve at $A$ and $B .$ The locus of the image of $P$ about $A B$ is

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Important Questions on Parabola

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 55

The equation of the tangent to the parabola

y^{2} = 12 x

at

(3, - 6)

is

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 56

The cartesian co-ordinates of the point on the parabola

y^{2} = x

whose parameter is

\frac{- 4}{3}

are

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 57

Consider the parabola

y^{2} = 4 x

. Let

P

and

Q

be points on the parabola where

P (4, - 4)

and

Q (9, 6) .

Let

R

be a point on the arc of the parabola between

P

and

Q .

Then, the area of

Δ P Q R

is largest when

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 58

A B

is a chord of the parabola

y^{2} = 4 a x

with vertex

A .

B C

is drawn perpendicular to

A B

meeting the axis at

C .

The projection of

B C

on the axis of the parabola is

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 59

The equation of a tangent to the parabola

y^{2} = 8 x

is

y = x + 2 .

The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 60

The locus of the vertices of the family of parabolas

y = \frac{a^{3} x^{2}}{3} + \frac{a^{2} x}{2} - 2 a

is

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 61

Let

P

be the point

(1, 0)

and

Q

be the point on

y^{2} = 8 x .

The locus of midpoint of

P Q

is

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Mathematics Crash Course COMEDK UGET>Chapter 10 - Parabola>Exercise 1>Q 62

The two ends of a latus rectum of a parabola are

(5, 8)

and

(- 7, 8)

. Then its focus is