Question

The intercept made by the circle x^2 + y^2 + 4x - 8y + c =0 on x - axis is 2 root 10 then c =? ​

Answer 1

Answer:

Given eqn of circle is

x²+y²+4x-8y+c=0

Intercept on x axis is = 2√g²-c,if the standard form of circle is ax²+by²+2gx+2fy+c=0

2√10= 2√g²-c

here 2g=4

g=2

=>√10=√4-c

squaring on both sides,

10=4-c

=> c=-6

Therefore c=-6

Answer 2

Answer:

The intercept made by the circle $x^{2}+y^2+4x-8y+c=0$ on the x-axis is $2\sqrt{10}$ then $c=-6$

Step-by-step explanation:

We have an equation of a circle $x^{2}+y^2+4x-8y+c=0$ that makes an intercept on the x-axis as $2\sqrt{10}$

Now we have to calculate the value of c

Step 1 of 2

The standard equation of a circle is $ax^2+by^2+2gx+2fy+c=0$ and

the intercept on the x-axis = $2\sqrt{g^2-c}$

and hereby comparing the standard equation of circle we get

$2g=4$

⇒$g=2$

Step 2 of 2

Now with the help of the equation $2\sqrt{g^2-c}$ we get

$2\sqrt{10}=2\sqrt{g^2-c$

⇒$\sqrt{10}=\sqrt{2^2-c$

Squaring on both sides we get

$10=4-c$

⇒c=-6

Hence the value of c is -6