JEE Advanced 2013 · Paper 2 · Mathematics Q46

MathematicsMultiple correct+3 / -1Question 46 of 60

Circle(s) touching $x$ -axis at a distance 3 from the origin and having an intercept of length $2\sqrt7$ on $y$ -axis is (are)

x^2+y^2-6x+8y+9=0

x^2+y^2-6x+7y+9=0

x^2+y^2-6x-8y+9=0

x^2+y^2-6x-7y+9=0

Answer and worked solution

Official answer: A, C

Centre and radius. Touching the x-axis at $(3,0)$ : centre $(3,k)$ , radius $|k|$ .

y-intercept. $2\sqrt{k^2-9}=2\sqrt7$ gives $k=\pm4$ .

Circles. $(x-3)^2+(y\mp4)^2=16$ : $x^2+y^2-6x\mp8y+9=0$ .

(A), (C)

Topics:Equation of a circle

JEE Advanced 2013 · Paper 2, Mathematics question 46