A variable circle is described to pass through (1, 0) and touch the line y = x. The locus of the centre of the circle is a parabola, whose length of latus rectum, is

Question

A variable circle is described to pass through (1, 0) and touch the line y = x. The locus of the centre of the circle is a parabola, whose length of latus rectum, is (A) 2 (B) √ 2 (C) (1/√2) (D) 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f56d16a38b415969cdb1d22ab33ea7ef-.png" /> CF = CN Ã locus of C is a parbola with focus at (1, 0) and directrix y = x ⇒ length of latus rectum = 2(distance from focus to directrix) =2((1/√2))=√2

Q. A variable circle is described to pass through $(1, 0)$ and touch the line $y = x$ . The locus of the centre of the circle is a parabola, whose length of latus rectum, is

2

$\sqrt{ 2}

$\frac{1}{2}$

1

$CF = CN Þ$ locus of C is a parbola with focus at $(1, 0)$ and directrix $y = x$
$\Rightarrow$ length of latus rectum = 2(distance from focus to directrix)
$= 2 (\frac{1}{2}) = 2$

Q. A variable circle is described to pass through (1,0) and touch the liney=x. The locus of the centre of the circle is a parabola, whose length of latus rectum, is

2

$\sqrt{ 2}

2​1​

1

CF=CNÞ locus of C is a parbola with focus at (1,0) and directrix y=x ⇒ length of latus rectum = 2(distance from focus to directrix) =2(2​1​)=2​

Q. A variable circle is described to pass through $(1, 0)$ and touch the line $y = x$ . The locus of the centre of the circle is a parabola, whose length of latus rectum, is

$\frac{1}{2}$

$CF = CN Þ$ locus of C is a parbola with focus at $(1, 0)$ and directrix $y = x$
$\Rightarrow$ length of latus rectum = 2(distance from focus to directrix)
$= 2 (\frac{1}{2}) = 2$