Find the equations of the tangent and the normal to the following curves at the indicated points.(i) y = x4 − bx3 + 13x2 − 10x + 5 at (0, 5) [NCERT](ii) y = x4 − 6x3 + 13x2 − 10x + 5 at x = 1 [NCERT, CBSE 2011](iii) y = x2 at (0, 0) [NCERT](iv) y = 2x2 − 3x − 1 at (1, −2)(v) y2=x34-xat 2, -2(vi) y = x2 + 4x + 1 at x = 3 [CBSE 2004](vii) x2a2+y2b2=1 at acosθ, bsinθ(viii) x2a2-y2b2=1 at asecθ, btanθ(ix) y2 = 4ax at am2,2am(x) c2 x2+y2=x2 y2 at ccosθ, csinθ(ix) xy = c2 at ct,ct(xii) x2a2+y2b2=1 at x1, y1(xiii) x2a2-y2b2=1 at x0, y0 [NCERT](xiv) x23+y23 = 2 at (1, 1) [NCERT](xv) x2 = 4y at (2, 1)(xvi) y2 = 4x at (1, 2) [NCERT](xvii) 4x2 + 9y2 = 36 at (3cosθ, 2sinθ) [CBSE 2011](xviii) y2 = 4ax at (x1, y1) [CBSE 2012](xix) x2a2-y2b2=1 at 2a,b [CBSE 2014]

Find the equations of the tangent and the normal to the following curv

1.	Find the equations of the tangent and the normal to the following curves at the indicated points.(i) y = x4 − bx3 + 13x2 − 10x + 5 at (0, 5) [NCERT](ii) y = x4 − 6x3 + 13x2 − 10x + 5 at x = 1 [NCERT, CBSE 2011](iii) y = x2 at (0, 0) [NCERT](iv) y = 2x2 − 3x − 1 at (1, −2)(v) y2=x34-xat 2, -2(vi) y = x2 + 4x + 1 at x = 3 [CBSE 2004](vii) x2a2+y2b2=1 at acosθ, bsinθ(viii) x2a2-y2b2=1 at asecθ, btanθ(ix) y2 = 4ax at am2,2am(x) c2 x2+y2=x2 y2 at ccosθ, csinθ(ix) xy = c2 at ct,ct(xii) x2a2+y2b2=1 at x1, y1(xiii) x2a2-y2b2=1 at x0, y0 [NCERT](xiv) x23+y23 = 2 at (1, 1) [NCERT](xv) x2 = 4y at (2, 1)(xvi) y2 = 4x at (1, 2) [NCERT](xvii) 4x2 + 9y2 = 36 at (3cosθ, 2sinθ) [CBSE 2011](xviii) y2 = 4ax at (x1, y1) [CBSE 2012](xix) x2a2-y2b2=1 at 2a,b [CBSE 2014]
Answer» Find the equations of the tangent and the normal to the following curves at the indicated points. (i) y = x⁴ − bx³ + 13x² − 10x + 5 at (0, 5) [NCERT] (ii) y = x⁴ − 6x³ + 13x² − 10x + 5 at x = 1 [NCERT, CBSE 2011] (iii) y = x² at (0, 0) [NCERT] (iv) y = 2x² − 3x − 1 at (1, −2) (v) $y^{2} = \frac{x^{3}}{4 - x} at (2, - 2)$ (vi) y = x² + 4x + 1 at x = 3 [CBSE 2004] (vii) $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 at (a \cos θ, b \sin θ)$ (viii) $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 at (a \sec θ, b \tan θ)$ (ix) y² = 4ax at $(\frac{a}{m^{2}}, \frac{2 a}{m})$ (x) $c^{2} (x^{2} + y^{2}) = x^{2} y^{2} at (\frac{c}{\cos θ}, \frac{c}{\sin θ})$ (ix) xy = c² at $(c t, \frac{c}{t})$ (xii) $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 at (x_{1}, y_{1})$ (xiii) $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 at (x_{0}, y_{0})$ [NCERT] (xiv) $x^{\frac{2}{3}} + y^{\frac{2}{3}}$ = 2 at (1, 1) [NCERT] (xv) x² = 4y at (2, 1) (xvi) y² = 4x at (1, 2) [NCERT] (xvii) 4x² + 9y² = 36 at (3cosθ, 2sinθ) [CBSE 2011] (xviii) y² = 4ax at (x₁, y₁) [CBSE 2012] (xix) $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 at (\sqrt{2} a, b)$ [CBSE 2014]

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