Question

Let $ax+by+c=0$ be a variable straight line, where $a,b$ and $c$ are $1^{st},3^{rd}$ and $7^{th}$ terms of an increasing $A.P$. Then, the variable straight line always passes through a fixed point, which lies on

• A. $x^2+y^2=13$
• B. $x^2+y^2=5$
• C. $y^2=4x$
• D. $3x+4y=9$

Answer 1

The correct option is A $x^2+y^2=13$

$a,b,c$ are $1^{st},3^{rd}$ and $7^{th}$ terms of an increasing $A.P.$ then
So, $b=a+(3-1)d=a+2d$
$c=a+(7-1)d=a+6d$
Then,
$3b-c=2a$ ---(1)
$2a-3b+c=0$ ---(2)
Then,
$ax+by+c=0$
Always passes through $(2,-3).$
Then $(2,-3)$ lies on $x^2+y^2=13$ by given options.