Mathematics Crash Course JEE Advanced>Chapter 8 - Circle>Exercise 1>Q 31

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Mathematics

IMPORTANT

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The real numbers $a$ and $b$ are distinct. Consider the circles $ω_{1} : {(x - a)}^{2} + {(y - b)}^{2} = a^{2} + b^{2}$ and $ω_{2} : {(x - b)}^{2} + {(y - a)}^{2} = a^{2} + b^{2} .$ Which of the following is/are true?

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Important Questions on Circle

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Mathematics

IMPORTANT

Mathematics Crash Course JEE Advanced>Chapter 8 - Circle>Exercise 1>Q 32

Consider two circles

S_{1} \equiv x^{2} + y^{2} + 8 x = 0

and

S_{2} \equiv x^{2} + y^{2} - 2 x = 0

. Let

∆ P Q R

be formed by the common tangents to circles

S_{1}

and

S_{2}

. Then which of the following hold(s) good?

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 8 - Circle>Exercise 1>Q 33

The point of contact of the tangent to the circle

x^{2} + y^{2} = 5

at the point

(1, - 2)

which touches the circle

x^{2} + y^{2} - 8 x + 6 y + 20 = 0

, is

(h, k)

then

(2 h^{2} + 3 k^{2})

is equal to

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Mathematics

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Mathematics Crash Course JEE Advanced>Chapter 8 - Circle>Exercise 1>Q 34

If the length of the tangent from any point on the circle

(x - 3)^{2} + (y + 2)^{2} = 5 r^{2}

to the circle

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

is

16

units, then the area between the two circles is

λ π

sq. units then

λ

is equal to