The equation of a tangent to the hyperbola 4x2 – 5y2 = 20 parallel to the line x – y = 2 is :
JEE · Math · previous-year question
- A.x $$-$$ y + 9 = 0
- B.x $$-$$ y $$-$$ 3 = 0
- C.x $$-$$ y + 1 = 0correct
- D.x $$-$$ y + 7 = 0
Answer
C. x $$-$$ y + 1 = 0
Explanation
Hyperbola $${{{x^2}} \over 5} - {{{y^2}} \over 4} = 1$$ slope of tangent = 1 equation of tangent y = x $$ \pm $$ $$\sqrt {5 - 4} $$ $$ \Rightarrow $$ y = x $$ \pm $$ 1 $$ \Rightarrow $$ y = x + 1 or $$ \Rightarrow $$ y = x $$-$$ 1
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