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Question

Find the equation of parabola whose
Focus is (2,3) and the directrix is x4y+3=0

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Solution

Let A(x,y) be the Pt. on the parabola
focus = (2,3) & eqn of directrix
x4y+3=0
Let us draw from A to the directrix
& this be AM (say)
Then, SA = AM
(SA)2=(AM)2
(x2)2+(y3)2=∣ ∣ ∣x4y+312+(4)2∣ ∣ ∣2
x24x+4+y26y+9=(x4y+3)217
17x2+17y268x102y+221=x2+16y2+98xy+6x24y
16x2+y2+8xy74x78y+212=0
Which is the required eqn of
parabola.

1135727_1144534_ans_7bcbd86274434707a226c4cd5101cb95.jpg

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