What is the equation of chord of contact of tangents drawn from P(10, 8) to the ellipse
x225+y216=1.
4x+5y=10
We have to find the equation of chord of contact for a point given. We can find it in two ways mainly. Using formula and comparing equations. The equation of chord of contact of a second degree curve is given by
T=0⇒10x25+8y16=1⇒2x5+y2=1⇒4x+5y=10
In the second method we will write the equation of two tangents assuming two points of contact, (x1,y1) and(x2,y2). The equations of tangents at these points are
⇒xx125+yy116=1 and xx225+yy216=1
Since these two lines pass through (10,8), we have 10x125+8y116=1 and 10x225+8y216=1
Comparing these two equations, we find that an equation of the form
10x25+8y16=1
will be satisfied by both (x1,y1) and (x2,y2). So the equation of line passing through these two points will be
10x25+8y16=1.
We will be using the formula based approach to solve problems. As you can see, it is less confusing and fast.