Question

Assertion :Statement-1: Equation of a circle through the origin and belonging to the co-axial system.of which the limiting points are $(1,1)$ and $(3,3)$ is $2x^2+2y^2-3x-3y=0$ Reason: Equation of a circle passing through the points $(1,1)$ and $(3,3)$ is $x^2+y^2-2x-6y+6=0$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Two members of the system of circles in statement-$1$ are the circles
with centres at the limiting points and radius equal to zero i.e.
$(x-1{)}^2+(y-1{)}^2=0$ and $(x-3{)}^2+(y-3{)}^2=0$
or $x^2+y^2-2x-2y+2=0$ and $x^2+y^2-6x-6y+18=0$
Equation of the co-axial system is
$x^2+y^2-6x-6y+18+\lambda (x^2+y^2-2x-2y+2)=0$
which passes though the origin if $\lambda =-9$
Thus the equation of the required circle is $2x^2+2y^2-3x-3y=0$
So the statement-$1$ is true.
Statement-$2$ is also true as the circle in it passes through$(1,1)$ and $(3,3)$ but does not lead to statement-$1$