Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 39

EASY

JEE Main

IMPORTANT

Earn 100

The equation of circle which has normals $(x - 1) (y - 2) = 0$ and a tangent $3 x + 4 y = 6$ is:

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Important Questions on Circle

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 40

If the straight line

y = m x

is outside the circle

x^{2} + y^{2} - 20 y + 90 = 0

, then

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 41

The equation

a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0

represents a circle if

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 42

If equation

x^{2} + y^{2} + 2 h x y + 2 g x + 2 f y + c = 0

represents a circle, then the condition for that circle to pass through three quadrants only but not passing through the origin is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 43

If the chord of contact of tangents from of a point

P

to a given circle passes through

Q

,then the circle on

PQ

as diameter

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 44

The point from which the tangents to the circle

x^{2} + y^{2} - 4 x - 6 y - 16 = 0,

3 x^{2} + 3 y^{2} - 18 x + 9 y + 6 = 0

and

x^{2} + y^{2} - 8 x - 3 y + 24 = 0

are equal in length is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 45

If the two circles

{(x - 1)}^{2} + {(y - 3)}^{2} = r^{2}

and

x^{2} + y^{2} - 8 x + 2 y + 8 = 0

intersect in two distinct points, then

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 46

The shortest distance from the point

(0, 5)

to the circumference of the circle

x^{2} + y^{2} - 10 x + 14 y - 151 = 0

is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 6 - Circle>6.1>Q 47

If the radius of the circle

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

and

{(x - 7)}^{2} + {(y - 10)}^{2} = 4

are increasing uniformly w. r. t. time as

0.3

and

0.4 unit / \sec

, then they will touch each other at

t

equal to