Math, asked by pri6621, 1 year ago

if y=mx+c and x²+y²=a² i)intersects at A and B ii)AB=2∆ then show that c²=(1+m²)(a²-∆²)


Answers

Answered by tharareddy37
4
See the image above. x^2 + y^2 =a^2 is a circle with center A(0,0) and radius a.
y = mx + c is equation for straight line. It touches the x axis at C(-c/m,0) and y axis at B(0,c).

For the line to touch the circle, it has to be a tangent as shown above (line BC). 
From the figure, Area of Triangle ABC = 1/2 * AC * AB = 1/2 * BC * AD
BC^2 =  AB^2 + AC^2 (Pythagoras Theorem)

So, squaring both sides, we have
(c/m)^2 * c^2 = (c^2+c^2/m^2) * a^2

Simplifying, we get a^2(m^2+1) = c^2
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Answered by pavankormana
1

Answer:

please explain in detail

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