Math, asked by sandipmaji, 1 year ago

Find the equation of parabola whose focus (3,-4) and directix 6x-7y+5=0 respectively

Answers

Answered by kvnmurty

For any point P(x,y) on the parabola, the distance to the focus F(3, -4) is equal to the perpendicular distance to the Directrix line D, 6x-7y+5=0.

$\frac{ {6x - 7y + 5}^2}{(6^2 + 7^2 )} = (x - 3)^2 + (y + 4)^2 \\ \\ 36 x^2 + 49 y^2 + 25 - 84xy - 70y + 60x = 85 x^2 + 85 y^2 - 510x - 2125 + 680y \\ \\ 49 x^2 + 36^2 + 84xy - 570x + 750y - 2150 = 0 \\ \\this \: is \: the \: parabola.$

.See the enclosed equation of the parabola.

kvnmurty: :-)

kvnmurty: If one end of a diameter of the circle x^2+y^2-4x-6y+11=0 is (8,4). Show that the coodinates of the other end are (-4,2).

kvnmurty: Find center of circle. .O=(2, 3).. P=(8,4)..O is midpoint of PQ Diameter.

kvnmurty: Q=(a,b).. So (a+8)/2=2. a=-4....(b+4)/2=3...So b=2.

kvnmurty: Okay?

sandipmaji: thnx

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