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Question

Mathematics Question on Conic sections

Length of intercept made by the circle x2+y216x+4y36=0x^{2} + y^{2} - 16x + 4y - 36 = 0 on xx-axis is

A

2020

B

1010

C

55

D

None of these

Answer

2020

Explanation

Solution

As the circle meet xx-axis at two points so put y=0y= 0 in the equation of circle, we get x216x36=0x^{2 }- 16x - 36 = 0 Let two roots of the equation be x1x_{1} and x2x_{2}. x1+x2=16 \Rightarrow\, x_{1}+x_{2}=16 and x1x2=36x_{1}x_{2}=-36 Now, x1x2=(x1+x2)24x1x2 x_{1}-x_{2}=\sqrt{\left(x_{1}+x_{2}\right)^{2}-4x_{1}x_{2}} =(16)2+(4×36)=400=20==\sqrt{\left(16\right)^{2}+\left(4\times36\right)}=\sqrt{400}=20 = Intercept on xx-axis