Find the eqn of the tangent to the curve x2 +2y = 8 which is perpendicular to the - Maths - Application of Derivatives

Question

Find the eqn of the tangent to the curve x2 +2y = 8
which is perpendicular to the line x-2y+1 =0

Ishwarmani · Accepted Answer

Dear Student, Please find below the solution to the asked query:given curve : x2 +  2y = 8      
igiven line : x - 2y = -1        
iilet the point of contact of the tangent to curve i perpendicular to lineiibe Pa,bdifferentiating i both sides w
r t
  x,2x + 2dydx = 0⇒dydx = -x⇒dydxa,b = -aslope of lineii = 12since tangent at a,b is perpendicular to line ii∴-a × 12 = -1⇒ a = 2∵Pa,b lies on the curvei∴a2 +  2b = 8⇒b= 2∴P ≡ 2,2equation of the tangent at P2,2 ⇒y - 2 = -2x - 2⇒2x + y -6 = 0Hope this information will clear your doubts about the topic
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Find the eqn. of the tangent to the curve x2 +2y = 8 which is perpendicular to the line x-2y+1 =0

Find the eqn. of the tangent to the curve x² +2y = 8 which is perpendicular to the line x-2y+1 =0