Question

The equation of a parabola is $25\{{(x-2)}^2+{(y+5)}^2\}={(3x+4y-1)}^2$. For this parabola

• A. vertex=$(2,-5)$
• B. focus=$(2,-5)$
• C. directrix has the equation $3x+4y-1=0$
• D. axis has the equation $3x+4y-1=0$

Answer 1

Answer: (B), (C)

focus=$(2,-5)$
directrix has the equation $3x+4y-1=0$

Given equation may be written as,
$(x-2{)}^2+(y+5{)}^2={\left|\frac{3x+4y-1}{\sqrt{3^2+4^2}}\right|}^2$
$\Rightarrow PS=PM$
so clearly focus $=(2,-5)$
and equation of directrix is $3x+4y-1=0$