Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 8

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IMPORTANT

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A line meets the co-ordinate axes in $A$ and $B .$ A circle is circumscribed about the triangle $O A B$ . If $d_{1}$ and $d_{2}$ are the distances of the tangent to the circle at the origin $O$ from the points $A$ and $B$ , respectively, then the diameter of the circle is

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Important Questions on Circle

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 9

Let the tangent to the circle

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

at the point

R (3, 4)

meet

x

-axis and

y

-axis at point

P

and

Q

, respectively. If

r

is the radius of the circle passing through the origin

O

and having centre at the incentre of the triangle

O P Q,

then

r^{2}

is equal to

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 10

The locus of the point of intersection of tangents to the circle

x^{2} + y^{2} = a^{2},

which are inclined at an angle

α

with each other, is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 11

If the circle

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

is touched by the line

y = x

at point

P

such that

O P = 6 \sqrt{2}

units, where

O

is the origin, then the value of

c

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 12

Let

|(n - a)! - t| + |t - (n - b)!| + |a + b - k_{1} n - k_{2}| \leq 0 \forall n

such that

a < b < n

and

a, b, n, t \in N & k_{1}, k_{2} \in I

. If

P, Q

be any two points on the curve

y = \log_{\frac{1}{2}} (x + \frac{k_{2}}{2}) + \log_{2} (\sqrt{4 x^{2} + 4 k_{2} x + (k_{1} + k_{2})})

. Also point

P

lies on

x^{2} + y^{2} = k_{1}^{3} - 2 k_{2}

and point

Q

lies inside the given circle such that its abscissa is an integer. Then the minimum value of

\vec{O P} . \vec{O Q}

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 4 - Circle>Level 3>Q 13

The point

P

moves in the plane of a regular hexagon, such that the sum of squares of its distances from the vertices of hexagon is

6 a^{2} .

If the radius of the circumcircle of hexagon is

r (< a),

then the locus of

P

is