For what value of c, the lines which join the origin to the points of intersection of the given straight line and the curve be at right angle?

For what value of c, the lines which join the origin to the points of intersection of straight line xy+c=0 and the curve x2+y2+4x6y36=0 be at right angle?

1 Answer
Mar 22, 2018

c=5±97

Explanation:

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Equation of the straight line perpendicular to the sraight line xy+c=0 and passing through the origin (0,0) will be x+y=0.

Let us solve for xandy to find out the coordinates of point of intersection of the straight line x+y=0 and the circle x2+y2+4x6y36=0
Inserting x=y in the equation of the circle we get

y2+y24y6y36=0

2y210y36=0

y25y18=0

y=5±524×1×(18)2

y=5±972

when y=5+972,then x=y=5+972

Now from given equation xy+c=0

we get c=yx=5+97

and

when y=5972,then x=y=5972

for this coordinate

c=yx=597