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```				    Find p and q so that y = 2 x is a tangent, line at x = 3, to the curve  y = p x 2 + q x + 2
```

6 years ago

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```										Dear nitin,

The point of tangency is on the tangent line y = 2x,  hence its y coordinate can also be calculated and its coordinates given by   (3 , 2(3)) = (3 , 6)
The above point of tangency is also on the curve  y = p x 2 + q x + 2, hence   6 = p(3) 2 + q (3) + 2
Let us now find y '   y ' = 2 p x + q
At x = 3 y ' is equal to the slope of the tangent line y = 2 x. Hence   2 = 2 p (3) + q
We now solve the two linear equations   9 p + 3 q = 4 and 6 p + q = 2
to find 9 p + 3 q = 4 and 6 p + q = 2   p = 2 / 9 and q = 2 / 3

We are all  IITians and here to help you in your IIT  JEE preparation.  All the best.

Sagar Singh
B.Tech IIT Delhi

```
6 years ago

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