A circle touching the x -axis at (.3,0.) and making an intercept of length 8 units on the y -axis, passes through the point

Question

A circle touching the x -axis at (.3,0.) and making an intercept of length 8 units on the y -axis, passes through the point (A) (.3,10.) (B) (.2,3.) (C) (.1,5.) (D) (.3,5.)

Tardigrade Admin · Accepted Answer

Equation of circles are beginarrayl(x-3)2+(y-5)2=25 (x-3)2+(y+5)2=25 endarray. <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-yoynflivvmoefhsb.jpg" /> ⇒ beginarraylx2+y2-6 x-10 y+9=0 x2+y2-6 x+10 y+9=0 endarray.

Q. A circle touching the $x$ -axis at $(3, 0)$ and making an intercept of length $8$ units on the $y$ -axis, passes through the point

$(3, 10)$

$(2, 3)$

$(1, 5)$

$(3, 5)$

Equation of circles are ${(x - 3)^{2} + (y - 5)^{2} = 25 (x - 3)^{2} + (y + 5)^{2} = 25$

$\Rightarrow {x^{2} + y^{2} - 6 x - 10 y + 9 = 0 x^{2} + y^{2} - 6 x + 10 y + 9 = 0$

Q. A circle touching the x -axis at (3,0) and making an intercept of length 8 units on the y -axis, passes through the point

(3,10)

(2,3)

(1,5)

(3,5)