From a point P, two tangents PA and PB are drawn to the hyp…

Maths Conic Sections NTA Abhiyas Question - Hyperbola Single Correct MCQ

Published on: August 13, 2026

From a point P, two tangents PA and PB are drawn to the hyperbola . If these tangents cut the coordinate axes at 4 concyclic points,then the locus of P is

x 2 -y 2 = |a 2 -b 2 |

x 2 - y 2 = a 2 + b 2

x 2 +y 2 = |a 2 -b 2 |

x 2 +y 2 = a 2 +b 2

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The correct answer is:

x 2 -y 2 = a 2 + b 2

Let the equation of tangents are

y = m 1 x + C 1 , and

y = m 2 x + C 2

which cuts the coordinate axes at E, F, G, H as shown in the figure

Now, OE x OG = OF x OH

Let P be (h, k) and equation of the tangent through P on the hyperbola is

(k 2 -mh) 2 = (a 2 m 2 -b 2 )

(h 2 - a 2 )m 2 - 2khm + k 2 + b 2 = 0

whose roots are m 1 and m 2

locus is x 2 - y 2 = a 2 + fr 2

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