The locus of centre of circle which cuts two perpendicular lines so that each intercept has given length, is a conic whose eccentricity is

Question

The locus of centre of circle which cuts two perpendicular lines so that each intercept has given length, is a conic whose eccentricity is (A) 1 (B) (1/√2) (C) √2 (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/9d76bfb4fbc5b2f2e2677bd2bcbb8e5f-.png" /> r 2=(l12/4)+ k 2=(l22/4)+ h 2 h 2- k 2=(l12-l2 2/4)

Q. The locus of centre of circle which cuts two perpendicular lines so that each intercept has given length, is a conic whose eccentricity is

1

$\frac{1}{2}$

$2$

None of these

$r^{2} = \frac{l _{1}^{2}}{4} + k^{2} = \frac{l _{2}^{2}}{4} + h^{2}$
$h^{2} - k^{2} = \frac{l _{1}^{2} - l _{2} ^{2}}{4}$

Q. The locus of centre of circle which cuts two perpendicular lines so that each intercept has given length, is a conic whose eccentricity is

1

2​1​

2​

None of these

r2=4l12​​+k2=4l22​​+h2 h2−k2=4l12​−l2​2​

$\frac{1}{2}$

$2$

$r^{2} = \frac{l _{1}^{2}}{4} + k^{2} = \frac{l _{2}^{2}}{4} + h^{2}$
$h^{2} - k^{2} = \frac{l _{1}^{2} - l _{2} ^{2}}{4}$