Conics - Question from Patel (1 Viewer)

[kevda1st]

Im having trouble with a couple of questions from the patel book, please help

1. show that the line lx + my + n = 0 touches the
ellipse X^2 / a^2 +y^2 /b^2 =1 , if a^2 . l^2 +b^2 . m^2 = n^2

2.find the equation of two tangents to the ellipse 16X^2 + 25Y^2 =400 which are parallel to the line y= x+ 2

3.The tangent to the hyperbola X^2 / a^2 - y^2 /b^2 =1 (general equation of a hyperbola) at P( a sec t, b tan t ) meets the asymptotes at A and B. Prove that P is the mid-point of AB

 

[Timothy.Siu]

2.find the equation of two tangents to the ellipse 16X^2 + 25Y^2 =400 which are parallel to the line y= x+ 2

32x+30y(dy/dx)=0
dy/dx=-32x/30y
tangent is parallel to line y=x+2 therefore -32x/30y=1 -32x=30y -16x=15y
y=-16x/15
sub into equation
x^2=9
x=+-3
y=-+3.2
tangnets are y+3.2=x-3 and y-3.2=x+3

 

[Aerath]

Question 3

 

[Aerath]

That last squiggle meant nothing.

 

[Aerath]

Question 1:

 

[kevda1st]

wow, thank you!!