Question
Question: If the tangents on the ellipse \[4{{x}^{2}}+{{y}^{2}}=8\] at the point \(\left( 1,2 \right)\) and \(...
If the tangents on the ellipse 4x2+y2=8 at the point (1,2) and (a,b) are perpendicular to each other, then a2 is equal to:
A. 1764
B. 172
C. 17128
D. 174
Solution
First we will start by converting the given equation of ellipse into its standard form and then we will find the equation of tangents at the given point (1,2) and (a,b) using the formula a2xx1+b2yy1=1 ; once we find both the tangents, we will then apply the theorem of perpendicular lines and find the variables.
Complete step by step answer:
We will start by converting the given equation of ellipse into its standard form that is: a2x2+b2y2=1
Now, we have the equation of ellipse given in the question as follows: 4x2+y2=8 ........... Equation 1.
Now we will divide the whole equation by 8 to convert it into its standard form: