Question

# The focal distance of a point on the parabola  $$y ^ { 2 } = 8 x$$  is  $$10.$$  Its coordinates are

A
(2,±2)
B
(3,±3)
C
(5,±5)
D
(8,±8)

Solution

## The correct option is D $$( 8 , \pm 8 )$$The equation of parabola is$$y^2=8x$$$$\Rightarrow$$  $$4a=8$$$$\therefore$$   $$a=2$$Then the co-ordinates of focus $$S$$ is $$(2,0).$$Given focal distance is $$10.$$$$\Rightarrow$$  $$x+2=10$$$$\Rightarrow$$  $$x=8$$$$\Rightarrow$$ $$y^2=8x$$$$\Rightarrow$$ $$y^2=8(8)$$$$\Rightarrow$$  $$y^2=64$$$$\therefore$$   $$y=\pm 8$$Hence, the co-ordinates are $$(8,\pm 8)$$Maths

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