If y = m 1 x + c 1 and y = m 2 x + c 2, m 1 ≠ m 2 are two common tangents of circle x2+y2=2 and parabola y 2= x, then the value of 8| m 1 m 2| is equal to

Question

If y = m 1 x + c 1 and y = m 2 x + c 2, m 1 ≠ m 2 are two common tangents of circle x2+y2=2 and parabola y 2= x, then the value of 8| m 1 m 2| is equal to (A) 3+4 √2 (B) -5+6 √2 (C) -4+3 √2 (D) 7+6 √2

Tardigrade Admin · Accepted Answer

C1: x2+y2=2 C2: y2=x Let tangent to parabola be y = mx +(1/4 m ). It is also a tangent of circle so distance from centre of circle (0,0) will be √2. |((1/4 m )/√1+ m 2)|=√2 ⇒ 1=32 m 2+32 m 4 by solving m 2=(3 √2-4/8), m 2=(-3 √2-4/8) text (rejected) m=± √(3 √2-4/8) so , 8| m 1 m 2|=3 √2-4

Q. If $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}, m_{1} \neq = m_{2}$ are two common tangents of circle $x^{2} + y^{2} = 2$ and parabola $y^{2} = x$ , then the value of $8 ∣ m_{1} m_{2} ∣$ is equal to

$3 + 42$

$- 5 + 62$

$- 4 + 32$

$7 + 62$

Q. If y=m1​x+c1​ and y=m2​x+c2​,m1​=m2​ are two common tangents of circle x2+y2=2 and parabola y2=x, then the value of 8∣m1​m2​∣ is equal to

3+42​

−5+62​

−4+32​

7+62​

Q. If $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}, m_{1} \neq = m_{2}$ are two common tangents of circle $x^{2} + y^{2} = 2$ and parabola $y^{2} = x$ , then the value of $8 ∣ m_{1} m_{2} ∣$ is equal to

$3 + 42$

$- 5 + 62$

$- 4 + 32$

$7 + 62$