A circle is drawn whose centre is on the x-axis and it touches the y-axis. If no part of the circle lies outside the parabola y2=8x, then the maximum possible radius of the circle is

Question

A circle is drawn whose centre is on the x-axis and it touches the y-axis. If no part of the circle lies outside the parabola y2=8x, then the maximum possible radius of the circle is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-smivpnibgzra.png" /> Let equation of circle is (x - r)2+y2=r2 Solving it with y2=8x, we get, x2-2rx+r2+8x=r2⇒ x=0 or x=2r-8 ⇒ rm a x i m u m=4

Q. A circle is drawn whose centre is on the $x - a x i s$ and it touches the $y - a x i s .$ If no part of the circle lies outside the parabola $y^{2} = 8 x,$ then the maximum possible radius of the circle is

Let equation of circle is $(x - r)^{2} + y^{2} = r^{2}$
Solving it with $y^{2} = 8 x,$ we get,
$x^{2} - 2 r x + r^{2} + 8 x = r^{2} \Rightarrow x = 0$ or $x = 2 r - 8$
$\Rightarrow r_{ma x im u m} = 4$

Q. A circle is drawn whose centre is on the x−axis and it touches the y−axis. If no part of the circle lies outside the parabola y2=8x, then the maximum possible radius of the circle is

Let equation of circle is (x−r)2+y2=r2 Solving it with y2=8x, we get, x2−2rx+r2+8x=r2⇒x=0 or x=2r−8 ⇒rmaximum​=4

Q. A circle is drawn whose centre is on the $x - a x i s$ and it touches the $y - a x i s .$ If no part of the circle lies outside the parabola $y^{2} = 8 x,$ then the maximum possible radius of the circle is

Let equation of circle is $(x - r)^{2} + y^{2} = r^{2}$
Solving it with $y^{2} = 8 x,$ we get,
$x^{2} - 2 r x + r^{2} + 8 x = r^{2} \Rightarrow x = 0$ or $x = 2 r - 8$
$\Rightarrow r_{ma x im u m} = 4$