Question

A ball moving around the circle x2 + y2 - 2x - 4y - 20 = 0 in anti-clockwise direction leaves it tangentially at the point P(-2,-2). After getting reflected from a straight line it passes through the centre of the
circle. Find the equation of this straight line if its perpendicular distance from P is 5/2 . You can assume that the angle of incidence is equal to the angle of reflection. If you know then answer otherwise plz don't answer.
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Answer 1

Answer:

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Step-by-step explanation:

x^2 + y^2 -2x - 4y - 20 =0 can be simplified into

x^2–2x+1=y^2–4y+4–25=0

(x-1)^2 + (y-2)^2=5^2

So we can see the centre of the circle is (1,2) and radius is 5.

As both the circles have radius 5, we can conclude that (5,5) is the midpoint of the line joining the centres of the two circles.

Let the centre of the required circle be (x,y)

Then we know that (x+1)/2=5

So x=9

(y+2)/2=5

So y=8.

So the centre of the required circle is (9,8)

equation of the circle is

(x-9)^2 + (y-8)^2=5^2

x^2 +81–18x+y^2+64–16y=25

x^2– 18x + y^2 -16y +120=0

This is the equation of the circle.

Answer 2

Answer:

tangentially at the point P(-2,-2). After getting reflected from a straight line it passes through the centre of the

circle. Find the equation of this straight line if its perpendicular distance from P is 5/2

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