PrepRung
Sign inSign up free

NDA 2022 Maths · Mathematics · Circles · hard

The circles x^2+y^2=9 and x^2+y^2-8x-6y+k=0 intersect orthogonally.

Single correct option

The circles x2+y2=9x^2+y^2=9 and x2+y2−8x−6y+k=0x^2+y^2-8x-6y+k=0 intersect orthogonally. The value of kk is
  1. A. 99
  2. B. −9-9
  3. C. 2525
  4. D. 1616
Show answer and solution

Answer: (A) 99

For orthogonal circles 2g1g2+2f1f2=c1+c22g_1g_2+2f_1f_2=c_1+c_2. Here g1=f1=0g_1=f_1=0, c1=−9c_1=-9, and the second circle has c2=kc_2=k. So 0=−9+k0=-9+k and k=9k=9. Note that −9-9 results from copying the sign of c1c_1 wrongly.
Report a mistake

Original question written in the NDA 2022 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake