Question bank/JEE Main/Mathematics

A common tangent to the conics x2 = 6y and 2x2 - 4y2 = 9, is

Ax + y = 1Bx - y = 1Cx + y =[IMAGE]Dx
- y = [IMAGE]

Show answer and solution▾

Let y = (mx + c) is tangent to x2 = 6y.
So, x2 - 6mx - 6c = 0
put disc = 0
⇒  c =[IMAGE] m2
∴ we get y = mx -[IMAGE] m2
Also, [IMAGE] So, using condition of tangency, we get [IMAGE] ⇒  m4 = 2m2 - 1    ⇒ m4 - 2m2 + 1 = 0
⇒ (m2 - 1)2 = 0 ⇒  m = ± 1
∴ For m = 1, we get x - y =[IMAGE]

Source: Grass-G / M-01 Mathematics Paper-1.docx