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  • If is a point on the parabola <img alt="\mathrm{y^2=4 a x}" src="https://entrancecorner.oncodecogs.co

If \mathrm{P} is a point on the parabola \mathrm{y^2=4 a x} such that the subtangent and subnormal at \mathrm{P} are equal, then the coordinates of \mathrm{P} are

Option: 1

\mathrm{(a, 2 a) \text { or }(a,-2 a)}


Option: 2

\mathrm{(2 a, 2 \sqrt{2} a) \text { or }(2 a,-2 \sqrt{2} a)}


Option: 3

\mathrm{(4 a,-4 a) \text { or }(4 a, 4 a)}


Option: 4

None of these 


Answers (1)

best_answer

Since the length of the subtangent at a point on the parabola is twice the abscissa of the point and the length of the subnormal is equal to semi-latus-rectum. Therefore if \mathrm{P(x, y)} is the required point, then \mathrm{ 2 x=2 a \Rightarrow x=a}

Now \mathrm{ (x, y)} lies on the parabola \mathrm{ y^2=4 a x \Rightarrow 4 a^2=y^2 \Rightarrow y= \pm 2 a}

Thus the required points are \mathrm{{ }{(a, 2 a)}} and \mathrm{(a,-2 a)}

 

Posted by

shivangi.bhatnagar

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