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  • Find the equations of the circles which touch the axis of y at (0,3) and make an intercept  of 8 units on the axis of x .Option: 1 <img alt

Find the equations of the circles which touch the axis of y at (0,3) and make an intercept  of 8 units on the axis of x .

Option: 1

\mathrm{x^2+y^2 \pm 10 x-3 y+5=0}


Option: 2

\mathrm{x^2+y^2 \pm 10 x-6 y+9=0}


Option: 3

\mathrm{x^2+y^2 \pm 10 x-6 y+8=0}


Option: 4

\mathrm{x^2+y^2+10 x+6 y-9=0}


Answers (1)

best_answer

Let the circle with the centre at C intersects x-axis at A  AND B.

Also let \mathrm{C L \perp A B} . Then

\mathrm{A B=8 \therefore A L=4 \text { and } L C=3}

\mathrm{\therefore } radius of the circle  \mathrm{=\sqrt{4^2+3^2}=5}

y-coordinate of C is =  3, 

x-coordinate is = ±5     (± radius)

∴ equations of the required circle are  

\mathrm{\begin{aligned} & (x \pm 5)^2+(y-3)^2=25 \\ & \text { i.e. } x^2 \pm 10 x+25+y^2-6 y+9=25 \\ & \text { i.e. } x^2+y^2 \pm 10 x-6 y+9=0 \end{aligned}}

 

 

Posted by

SANGALDEEP SINGH

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