Question

the equation of parabola having focus (-3, 4) and directrix x=2 is​

Answer 1

Answer:

Step-by-step explanation:

Given, the focus of the parabola S ≡ (-3, 4) and the directrix x=2

Let P(x,y) be any point on the parabola, then, its equation is given by

$\tt{SP=PM}$

Where PM is the perpendicular distance of the point P from the directrix

So,

$\sf{\sqrt{(x+3)^2+(y-4)^2}=\dfrac{|x-2|}{1}}$

$\sf{\implies(\sqrt{(x+3)^2+(y-4)^2}\,)^2=(|x-2|)^2}$

$\sf{\implies(x+3)^2+(y-4)^2=(x-2)^2}$

$\sf{\implies\,x^2+6x+9+y^2-8y+16=x^2-4x+4}$

$\sf{\implies\,6x+9+y^2-8y+16=-4x+4}$

$\sf{\implies\,10x+9+y^2-8y+16-4=0}$

$\sf{\implies\,10x+5+(y^2-8y+16)=0}$

$\sf{\implies\,10\bigg(x+\dfrac{1}{2}\bigg)+(y-4)^2=0}$

$\sf{\implies\,(y-4)^2=-10\bigg(x+\dfrac{1}{2}\bigg)}$