Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 82

HARD

JEE Main

IMPORTANT

Earn 100

A circle touches the hypotenuse of a right-angled triangle at its middle point and passes through the mid-point of the shorter side. If $a$ and $b (a < b)$ be the lengths of the sides, then prove that the radius of the circle is $\frac{a}{2 b} \sqrt{a^{2} + b^{2}}$ .

Important Questions on Circle

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 84

Show that the circumcircle of the triangle formed by three lines

x \cos α_{r} + y s i n α_{r} = p_{r}, r = 1,2, 3

will pass through the origin if

\sum p_{1} p_{2} \sin (α_{1} - α_{2}) = 0 .

MEDIUM

JEE Main

IMPORTANT

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

If two distinct chords drawn from the point

(p, q)

on the circle

x^{2} + y^{2} = p x + q y

(where

p q \neq 0

) are bisected by the

x

-axis, then

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 2

The triangle

P Q R

is inscribed in the circle

x^{2} + y^{2} = 25

. If

Q

and

R

have coordinates

(3, 4)

and

(- 4, 3)

respectively, then

∠ Q P R

is equal to

MEDIUM

JEE Main

IMPORTANT

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

If the circle

x^{2} + y^{2} + 2 x + 2 k y + 6 = 0

and

x^{2} + y^{2} + 2 k y + k = 0

intersect orthogonally, then

k

is equal to

EASY

JEE Main

IMPORTANT

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

The equation of the tangents drawn from the origin to the circle

x^{2} + y^{2} - 2 p x - 2 q y + q^{2} = 0

are perpendicular if

EASY

JEE Main

IMPORTANT

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

The equation of the circle passing through

(1, 0)

and

(0, 1)

and having smallest possible radius is

MEDIUM

JEE Main

IMPORTANT

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

The square of the length of the tangent from

(3, - 4)

to the circle

x^{2} + y^{2} - 4 x - 6 y + 3 = 0

, is

MEDIUM

JEE Main

IMPORTANT

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

The length of the common chord of the circles

x^{2} + y^{2} + 2 x + 3 y + 1 = 0

and

x^{2} + y^{2} + 4 x + 3 y + 2 = 0

is