Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 18

HARD

JEE Main/Advanced

IMPORTANT

Earn 100

A square is inscribed in the circle $x^{2} + y^{2} - 10 x - 6 y + 30 = 0 .$ One side of the square is parallel to $y = x + 3$ , then the vertex of the square is:

50% studentsanswered this correctly

Important Questions on Circle

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>Multiple Choice II>Q 19

If point

P (x, y)

is called a lattice point if

x, y \in I

. Then the total number of lattice points in the interior of the circle

x^{2} + y^{2} = a^{2}, a \neq 0

can not be :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 1

If a variable circle touches externally two given circles, then the locus of the centre of the variable circle is _____

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 2

If point

P (x, y)

is called a lattice point if

x, y \in I

. Then the total number of lattice point in the interior of the circle

x^{2} + y^{2} = a^{2}, a \neq 0

is of the form

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 3

A square is inscribed in the circle

x^{2} + y^{2} - 10 x - 6 y + 30 = 0 .

One side of the square is parallel to

y = x + 3

, then the vertex of the square is:

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 4

If a chord of the circle

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

makes equal intercepts of length

a

on the co-ordinate axes, then

|a| <

______

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 5

The values of

λ

for which the circle

x^{2} + y^{2} + 6 x + 5 + λ (x^{2} + y^{2} - 8 x + 7) = 0

dwindles into a point are _____

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 6

The radical centre of three circles described on the three sides of a triangle as diameter is_____

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 4 - Circle>FILL IN THE BLANKS>Q 7

Origin is a limiting point of co-axial system of which

x^{2} + y^{2} - 6 x - 8 y + 1 = 0

is a member. The other limiting point is _____