AP EAMCET · Maths · Application of Derivatives
The curves \(y=x^2-1, y=8 x-x^2-9\)
- A intersect at right angles at \((2,3)\)
- B touch each other at \((2,3)\)
- C intersect at \(45^{\circ}\)
- D intersect at \(60^{\circ}\)
Answer & Solution
Correct Answer
(B) touch each other at \((2,3)\)
Step-by-step Solution
Detailed explanation
\(y=x^2-1\) \(\Rightarrow \quad y=8 x-x^2-9\) For point of intersection, \(x^2-1=8 x-x^2-9\) \(2 x^2-8 x+8=0\) \(\Rightarrow \quad x^2-4 x+4=0\) \(\Rightarrow \quad(x-2)^2=0\) \(\Rightarrow \quad x=2\) \(\therefore \quad y=2^2-1=3\) Point of intersection \(=(2,3)\)…
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