Let P(6,3) be a point on the hyperbola parabola `x^2/a^2-y^2/b^2=1`If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is
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To find the eccentricity of the hyperbola given the point P(6, 3) and the condition that the normal at this point intersects the x-axis at (9, 0), we will follow these steps:
### Step 1: Write the equation of the normal at point P(6, 3)
The equation of the normal to the hyperbola at a point \((x_0, y_0)\) is given by:
\[
\frac{a^2 x}{x_0} + \frac{b^2 y}{y_0} = a^2 + b^2
\]
Substituting \(x_0 = 6\) and \(y_0 = 3\):
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