Find the co-ordinates of the point on the curve y=x^2+3x+4 the tangent passes through origin.

Hi,

Find the slope of tangent by differentation. The slope will be 2x+3, Here x is the point on the curve. Let it be h. So slope will he 2h+3. Equation of tangent passing through origin will be y = (2h+3)x.

Put the value of tangent in the curve and make discriminent zero as the tangent and curve has onl;y one solution. You wilol get h as +2 and -2, corresponding y coordinates will be +14 and +2.

So coordinates are 2, 14 and -2, 2.