AB is a focal chord of x2 - 2x + y - 2 = 0 whose focus is S. If AS = l1. then BS is equal to

Question

AB is a focal chord of x2 - 2x + y - 2 = 0 whose focus is S. If AS = l1. then BS is equal to (A) l1 (B) (4l1/4l1 -1) (C) (l1/4l1 -1) (D) (2l1/4l1 -1)

Tardigrade Admin · Accepted Answer

Given curve is x2 - 2x + y - 2 = 0 ⇒ x2 - 2x + y - 2 +1 = 1 ⇒ (x -1)2 = - y + 3 = -1( y - 3) which is downward parabola with a = (1/4) We know, if l1 and l2 are the length of the segment of any focal chord then length of semi-latus rectum is (2l1l2/l1+l2) Here AS =l1 and BS = l2 (say) are the segments. ∴ we have (2l1(BS)/l1+BS) = 2a ⇒ BS = (l1/4l1 - 1)

Q. AB is a focal chord of $x^{2} - 2 x + y - 2 = 0$ whose focus is S. If $A S = l_{1}$ . then BS is equal to

$l_{1}$

$\frac{4 l _{1}}{4 l _{1} - 1}$

$\frac{l _{1}}{4 l _{1} - 1}$

$\frac{2 l _{1}}{4 l _{1} - 1}$

Q. AB is a focal chord of x2−2x+y−2=0 whose focus is S. If AS=l1​. then BS is equal to

l1​

4l1​−14l1​​

4l1​−1l1​​

4l1​−12l1​​

Q. AB is a focal chord of $x^{2} - 2 x + y - 2 = 0$ whose focus is S. If $A S = l_{1}$ . then BS is equal to

$l_{1}$

$\frac{4 l _{1}}{4 l _{1} - 1}$

$\frac{l _{1}}{4 l _{1} - 1}$

$\frac{2 l _{1}}{4 l _{1} - 1}$