Tangent and Normal
Find the equations of the tangents to the ellipse $x^{2} + 3 y^{2} = 4$ which are perpendicular to the line 3x+y=7,
Ans: $x - 3 y = \pm 4$

Question

Tangent and Normal
Find the equations of the tangents to the ellipse x 2 + 3 y 2 = 4
which are perpendicular to the line 3x+y=7,
Ans: x - 3 y = ± 4

Aarushi Mishra · Accepted Answer

E: x2+3y2=4d (x2+3y2)d x=d 4dx2x+6ydydx=0dydx=-x3yLet the point on ellipse be P(x1,y1)dydxat P=-x13y1Given line 3x+y=7 has slope m1=-3For perpendicular lines m1m2=-1m2=13, this is slope of tangnent-x13y1=13x1=-y1 _____________(1)Solving this equation with ellipesex12+3x12=44x12=4x1=±1if x1=1 then y1=-1orif x1=-1 then y1=1Equation of tangnents, using two point form(y+1)=13(x-1)3y-x+4=0or(y-1)=13(x+1)3y-x-4=0

Tangent and Normal Find the equations of the tangents to the ellipse x 2 + 3 y 2 = 4 which are perpendicular to the line 3x+y=7, Ans: x - 3 y = ± 4

Tangent and Normal
Find the equations of the tangents to the ellipse $x^{2} + 3 y^{2} = 4$ which are perpendicular to the line 3x+y=7,
Ans: $x - 3 y = \pm 4$