Q.1. The slope of the tangent at the point (2,-2) to the curve x2 + xy + y2-4 = 0 is:
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EXPLANATION.
→ slope of the tangent at the point ( 2,-2) to
the curve = x² + xy + y² - 4 = 0
→ differentiate w.r.t x
→ 2x + x. dy/dx + y + 2y.dy/dx - 0 = 0
→ ( 2x + y) + ( x + 2y )dy/dx = 0
→ put the value of the point (2,-2)
→ [(2(2) + (-2) ] + [ 2 + 2(-2)] dy/dx = 0
→ [ 2 ] + [ -2 ]dy/dx = 0
→ 2 = 2.dy/dx
→ dy/dx = 1 = slope
More information.
→ equation of tangent.
→ ( y - y¹ ) = m ( x - x¹ )
→ ( y - (-2)) = 1 ( x - 2 )
→ ( y + 2 ) = x - 2
→ y - x = -4
→ equation of normal.
→ ( y - y¹ ) = -1/m ( x - x¹ )
→ ( y + 2 ) = - ( x - 2 )
→ y + 2 = - x + 2
→ y + x = 0
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