Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 17

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The equation of a circle $S_{1}$ is $x^{2} + y^{2} = 1$ . The orthogonal tangents to $S_{1}$ meet at another circle $S_{2}$ and the orthogonal tangents to $S_{2}$ meet at the third circle $S_{3}$ . Then

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Important Questions on Circle

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JEE Main

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 18

A point

P (\sqrt{3}, 1)

moves on the circle

x^{2} + y^{2} = 4

and after covering a quarter of the circle, leaves it tangentially. The equation of a line along which the point moves after leaving the circle is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 19

A (\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}})

is a point on the circle

x^{2} + y^{2} = 1

and

B

is another point on the circle such that

AB = \frac{π}{2}

units. Then coordinates of

B

can be

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 1

From a point

P

outside a circle with center at

C,

tangents

P A

and

P B

are drawn such that

\frac{1}{{(C A)}^{2}} + \frac{1}{{(P A)}^{2}} = \frac{1}{16}

, then the length of chord

A B

is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 3

If

11 a^{2} + 2 b^{2} + 2 a k + 1 = 0

, where

k

is a fixed real number, then the value of

k^{4}

for which

a x + b y + 1 = 0

is tangent to a fixed circle is ...

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 4

The extremities of a diagonal of a rectangle are

(- 4, 4)

and

(6, - 1)

. A circle circumscribes the rectangle and cuts an intercept

A B

on the

y

-axis. If

Δ

be the area of the triangle formed by

A B

and the tangents to the circle at

A

and

B

, then

8 Δ =

.

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 5

A rectangle

A B C D

is inscribed in a circle with a diameter lying along the line

3 y = x + 10

. If

A

and

B

are the points

(- 6, 7)

and

(4, 7)

respectively, then area of rectangle

A B C D

in square units is ....

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 6

If curves

a_{1} x^{2} + 2 h_{1} x y + b_{1} y^{2} - 2 g_{1} x - 2 f_{1} y + c = 0

and

a_{2} x^{2} - 2 h_{2} x y + (a_{2} + a_{1} - b_{1}) y^{2} - 2 g_{2} x - 2 f_{2} y + c = 0

intersect in four concyclic points

A, B, C

and

D

and

H

be the point

(\frac{g_{1} + g_{2}}{a_{1} + a_{2}}, \frac{f_{1} + f_{2}}{a_{1} + a_{2}})

, then

\frac{5 H A^{2} + 7 H B^{2} + 8 H C^{2}}{H D^{2}} = \dots .

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 7

The least positive integral value of

λ

for which two chords bisected by

x

-axis can be drawn to the circle

x^{2} + y^{2} - λ a x - a y - a^{2} (λ^{2} + 1) = 0

from point

(a (λ - 1), a (λ + 1))

is ...