Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 2

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IMPORTANT

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The shortest distance between the line $x - y = 1$ and the curve $x^{2} = 2 y$ is:

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Important Questions on Parabola

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 3

The equation of one of the common tangents to the parabola

y^{2} = 8 x

and

x^{2} + y^{2} - 12 x + 4 = 0

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 4

Two tangents are drawn from

(p, q)

to the parabola

y^{2} = 8 x

such that the slope of one of the tangent is thrice of the other, then

\frac{3 q^{2}}{p} =

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 5

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 JEE Main>Chapter 20 - Parabola>Level 2>Q 6

If normals are drawn from a point

P (h, k)

to the parabola

y^{2} = 4 a x,

then the sum of the intercepts which the normals cut off from the axis of the parabola is

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 8

If the normal to a parabola $y^{2} = 4 a x$ at $P$ meets the curve again in $Q$ and if $P Q$ and the normal at $Q$ makes angle $α$ and $β,$

respectively, with the $x$ -axis, then $\tan α (\tan α + \tan β)$ has the value equal to

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 9

A line is a common tangent to the circle

{(x - 3)}^{2} + y^{2} = 9

and the parabola

y^{2} = 4 x

. If the two points of contact

(a, b)

and

(c, d)

are distinct and lie in the first quadrant, then

2 (a + c)

is equal to ___ .

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 10

Let

P, Q

be the points with parameters

t_{1}, t_{2}

on the parabola

y^{2} = 4 a x .

If the normals at

P, Q

meet on the parabola at

R (t_{3}),

then

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 13

If

L

is the minimum distance between the curves

{(x - 6)}^{2} + y^{2} = 5

and

y^{2} = 4 x

, then the value of

L^{2}

is