Question

If m =9x²-4xy+5y² and n = -3x²+2xy-y². Find (i) 2m-n (ii) m+2n (iii) m-3n​

Answer 1

Step-by-step explanation:

The tangent equations are:

At (1,2)    ⇒y=−45x+145

At (−1,3)⇒y=−15x+145

Explanation:

The gradient of the tangent to a curve at any particular point is given by the derivative of the curve at that point. The normal is perpendicular to the tangent so the product of their gradients is −1

We have:

x2+xy+y2=7

First let us check that (1,2) and #(-1,3) lies on the curve:

(1,2)    ⇒1+2+4=7

(−1,3)⇒1−3+9=7

Then differentiating (implicitly) wrt x, and applying the product rule gives us:

2x+xdydx+y+2ydydx=0

∴(2x+y)+(2y+x)dydx=0

∴dydx=−2x+y2y+x

Coordinate