Let the latus ractum of the parabola y2-4x be the common chord to the circles C1 and C2 each of them having radius 2-5- Then- the distance between the centres of the circles C1 and C2 is-

Length of latus rectum = 4 ⇒ AB=2 Given, C_1B=C_2B=2√(5) Now, (C_1 A )^2+4=(2√(5) )^2 ⇒ C_1 A=4 ⇒ C_1C_2=2C_1A=8 nbsp; ...

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Byju's Answer

Standard VIII

Mathematics

Equation of Circle with Origin as Center

Let the latus...

Question

Let the latus ractum of the parabola $y^{2} = 4 x$ be the common chord to the circles $C_{1}$ and $C_{2}$ each of them having radius $2 \sqrt{5}$ . Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ is:

8

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8 \sqrt{5}

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4 \sqrt{5}

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12

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Solution

The correct option is A $8$

Length of latus rectum $= 4$
$\Rightarrow A B = 2$

Given, $C_{1} B = C_{2} B = 2 \sqrt{5}$
Now, ${(C_{1} A)}_{1}^{2} + 4 = {(2 \sqrt{5})}^{2}$
$\Rightarrow C_{1} A = 4$
$\Rightarrow C_{1} C_{2} = 2 C_{1} A = 8$

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Let the latus ractum of the parabola y2=4x be the common chord to the circles C1 and C2 each of them having radius 2√5. Then, the distance between the centres of the circles C1 and C2 is:

The correct option is A 8 Length of latus rectum =4 ⇒AB=2 Given, C1B=C2B=2√5 Now, (C1A)2+4=(2√5)2 ⇒C1A=4 ⇒C1C2=2C1A=8

Let the latus ractum of the parabola $y^{2} = 4 x$ be the common chord to the circles $C_{1}$ and $C_{2}$ each of them having radius $2 \sqrt{5}$ . Then, the distance between the centres of the circles $C_{1}$ and $C_{2}$ is:

The correct option is A $8$

Length of latus rectum $= 4$
$\Rightarrow A B = 2$

Given, $C_{1} B = C_{2} B = 2 \sqrt{5}$
Now, ${(C_{1} A)}_{1}^{2} + 4 = {(2 \sqrt{5})}^{2}$
$\Rightarrow C_{1} A = 4$
$\Rightarrow C_{1} C_{2} = 2 C_{1} A = 8$