If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ intersect in two distinct points $P$ and $Q$ then the line $5 x + b y - a = 0$ passes through $P$ and $Q$

exactly one value of

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

no value of

a

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

infinity many values of

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

exactly two values of

a

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B no value of $a$
$S_{1} = x^{2} + y^{2} + 2 a x + c y + a = 0$

$S_{2} = x^{2} + y^{2} - 3 a x + d y - 1 = 0$

$S_{1} - S_{2} = 0 \Rightarrow 5 a x + (c - d) y + a + 1 = 0$

on comparing with $5 x + b y - a = 0$

$\frac{5 a}{5} = \frac{c - d}{b} = \frac{a + 1}{- a} \Rightarrow a (- a) = a + 1$

$a^{2} + a + 1 = 0$
No value of a.

Suggest Corrections

Similar questions

If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0 a n d x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P andn Q then the line 5x + by - a = 0 passes through P and Q for
(2005)

Q. lf the circles

x^{2} + y^{2} + 2 a x +

+ a = 0

and

x^{2} + y^{2} - 3 a x + d y - 1 = 0

intersect in two distinct points

P

and

Q

then the line

5 x + b y - a = 0

passes through

P

and

Q

for

If the circles $x^{2} + y^{2} + 2 a x + c y + a = 0$ and $x^{2} + y^{2} - 3 a x + d y - 1 = 0$ interesect in two distinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
(2005)