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Question

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


A
(2,±2)
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B
(3,±3)
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C
(5,±5)
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D
(8,±8)
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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 $$(8,\pm 8)$$


1495110_1208245_ans_35a4820c90e44aff8d3db2e6248ad284.jpeg

Maths

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