Question

The centre of a circle is (2x-1, 3x + 1) and radius is 10 units. Find the value of x if the circle passes through the point (-3,-1).​

Answer 1

Solution☞

Given: The centre of a circle is (2x-1, 3x + 1) and radius is 10 units. Find the value of x if the circle passes through the point (-3,-1).

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To find:the value of x if the circle passes through the point (-3,-1).

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Let's solve=>

We know that the radius of Circle is the distance between the center and at any point on the circle.

So we have r=OA

=>OA=10

=>OA²=100

=>(2x-1-(-3))²+(3x+1-(-1))²=100

=>(2x+2)²+(3x+2)²=100

=>4x²+8x+4+9x²+12x+4=100

=>13x²+20x+8=100

=>13x²+20x+8-100=0

=>13x²+20x-92=0

=>13x²-26x+46x-92=0

=>13x(x-2)+46(x-2)=0

=>(13x+46)(x-2)=0

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=>13x+46=0

OR

x-2=0

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13x=-46

OR

x=2

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=>x=-46/13

OR

=>x=2

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:.The values of the x are -46/13 or 2

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HOPE HELPFUL FROM MY SIDE...