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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Hyperbola

NTA Abhyas 2020 · Mathematics · Hyperbola

Values of m , for which the line y = mx + 2 5 is a tangent to the...

Values of mm, for which the line y=mx+25y = mx + 2\sqrt{5} is a tangent to the hyperbola 16x2−9y2=14416{x}^{2} - 9{y}^{2} = 144, are the roots of the equation x2−(a+b)x−4=0,{x}^{2} - \left(a + b\right)x - 4 = 0, then the value of \left(a + b\right) is equal to

Correct answer

0

Step-by-step solution

Equation of hyperbola is x29−y216=1.\dfrac{{x}^{2}}{9} - \dfrac{{y}^{2}}{16} = 1 .
Equation of tangent is y=mx+9m2−16y = mx + \sqrt{9{m}^{2} - 16}

⇒9m2−16=25⇒m=±2⇒ \sqrt{9{m}^{2} - 16} = 2\sqrt{5} ⇒ m = \pm 2
⇒a+b=⇒ a + b = sum of roots =0.= 0 .

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