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Prove that the curves y 2 = 4x and x 2 + y 2 – 6x + 1 = 0 touch each other at the point (1, 2).

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2 months ago

## Answers : (1)

Anand Kumar Pandey
2803 Points
```							Dear StudentIt is given thatcurve equations are:y^2= 4x....(1)andx^2+y^2–6x+ 1 = 0..... (2)differentiating (i) w.r.t. x, we get2y.(dy/dx) = 4⇒dy/dx = 2/ySlope of tangent at (1, 2),m1= 2/2 = 1Differentiating (ii) w.r.t. x, we get2x + 2y.(dy/dx)–6 = 02y. dy/dx = 6–2x⇒dy/dx = (6–2x)/ 2yHence, the slope of the tangent at the same point (1, 2)⇒m2= (6–2 x 1)/ (2 x 2) = 4/4 = 1It can be seen thatm1= m2= 1 at the point (1, 2).Thus, the given circles touch each other at the same point (1, 2).Thanks
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2 months ago
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### Course Features

• 51 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions