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Find the equation of a parabola whose fo...

Find the equation of a parabola whose focus is `(-8,-2)` and equation of directrix is `y = 2x-9`.

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Let the focus is S(-8,-2) and P(x,y) be any point on the parabola. Now from the definition of parabola.
SP=distance of P from directrix
`rArr""sqrt((x+8)^(2)+(y+2)^(2))=(2x-y-9)/(sqrt(2^(2)+(-1)^(2)))`
`rArr5(x^(2)+16x+64+y^(2)+4y+4)=4x^(2)+y^(2)+81-4xy-36x+18y`
`rArrx^(2)+4y^(2)+4xy+116x+2y+259=0`
which is the required equation of parabola.
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