Home
Class 12
MATHS
Find the equation to the pair of straigh...

Find the equation to the pair of straight lines joining the origin to the intersections oi the straight line `y=mx + c` and the curve `x^2 + y^2=a^2` . Prove that they are at right angles if `2c^2=a^2(1+m^2)`.

Text Solution

Verified by Experts

The correct Answer is:
`therefore " "2c^2=a^2(1+m^2)`
which is the required condition .
Promotional Banner

Topper's Solved these Questions

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 1|9 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

Similar Questions

Explore conceptually related problems

The pair of straight lines joining the origin to the points of intersection of the line y=2sqrt(2x)+c and the circle x^2+y^2=2 1 are at right angles , if

The equation of the straight line joining the origin to the point of intersection of y-x+7=0 and y+2x-2=0 is

Prove that the straight lines joining the origin to the points of intersection of the straight line hx+ky=2hk and the curve (x-k)^(2)+(y-h)^(2)=c^(2) are at right angle if h^(2)+k^(2)=c^(2) .

Find the equation of the lines joining the origin to the points of intersection of the line x+y=1 with the curve 4x^(2)+4y^(2)+4x-2y-5=0 and show that they are at right angles

If the lines joining the origin to the points of intersection of the line y=mx+2 and the curve x^(2)+y^(2)=1 are at right-angles, then

The equation of pair of straight lines joining the point of intersection of the curve x^2+y^2=4 and y-x=2 to the origin , is

If the lines joining the origin to the intersection of the line y=nx+2 and the curve x^2+y^2=1 are at right angles, then the value of n^2 is

The equation to the pair of lines joining the origin to the points of intersection of y=x+3 and 2x^(2)+2y^(2)=1 is

Find the equation of the straight lines passing through the origin making an angle alpha with the straight line y=mx+c .