If b and c are the lengths of the scgments of any focal chord of a parabola y2=4 a x, then the length of the semi-latus rectum is :

Question

If b and c are the lengths of the scgments of any focal chord of a parabola y2=4 a x, then the length of the semi-latus rectum is : (A) (b c/b+c) (B) √b c (C) (b+c/2) (D) (2 b c/b+c)

Tardigrade Admin · Accepted Answer

Since the semi latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola. ∴ l is the harmonic mean between b and c. Hence, l=(2 b c/b+c)

Q. If $b$ and $c$ are the lengths of the scgments of any focal chord of a parabola $y^{2} = 4 a x$ , then the length of the semi-latus rectum is :

$\frac{b c}{b + c}$

$b c$

$\frac{b + c}{2}$

$\frac{2 b c}{b + c}$

Since the semi latus rectum of a parabola is the harmonic mean between the segments of any focal chord of the parabola.
$∴ l$ is the harmonic mean between $b$ and $c$ .
Hence, $l = \frac{2 b c}{b + c}$

Q. If b and c are the lengths of the scgments of any focal chord of a parabola y2=4ax, then the length of the semi-latus rectum is :

b+cbc​

bc​

2b+c​

b+c2bc​