Question

Observe the following statements:
I. The circle $x^2+y^2-6x-4y-7=0$ touches y-axis
II. The circle $x^2+y^2+6x+4y-7=0$ touches x-axis
Then, which of the following statements is/are correct?

• A. Both I and II
• B. Neither I nor II
• C. Only I
• D. Only II

Answer 1

The correct option is B Neither I nor II

$x^2+y^2-6x-4y-7=0$

As general equation of circle is

${(x-h)}^2+{(y-k)}^2=a^2$

If circle touches y- axis,then

h=a,

:-${(x-a)}^2+{(y-k)}^2=a^2$

${(x-3)}^2+{(y-2)}^2={\left(2\sqrt{5}\right)}^2$

$a=2\sqrt{5}$

$h=3$

$h\ne a$

Hence condition doesn’t satisfy, which means $x^2+y^2-6x-4y-7=0$ doesn't touches y-axis.

$x^2+y^2+6x+4y-7=0$

${(x+3)}^2+{(y+2)}^2={\left(2\sqrt{5}\right)}^2$

If circle touches x axis then

$k=a$

$k\ne a$

As ,$k=-2$

$a=2\sqrt{5}$

Hence condition doesn’t satisfy, which means$x^2+y^2+6x+4y-7=0$ doesn't touches x- axis.

Thus option B is correct.