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The length of the perpendicular from the...

The length of the perpendicular from the origin, on the normal to the curve, `x^2 + 3xy - 10 y^2 = 0` at the point (2,1) is :

A

`3sqrt(5)`

B

3

C

`sqrt(5)`

D

`(2)/(sqrt(5))`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^2 + 3xy - 10 y^2 =0`
`m_N = ` slope of normal drawn to curve at (2,1) is -2
L: 2x + y =5
Perpendicular distance of L from (0,0) `=(|0+0-5|)/(sqrt(5)) =5/(sqrt(5))`
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