Question

Tangents are drawn from a point on the circle x²+y²=50 to the ellipse x²/30 +y²/20=1, the tangents are at an angle..........

Answer 1

the equation of the given circle is x2+y2=25⇒x2+y2=52 .......(1)
the coordinates of any point on the circle is given by;P (5cosθ,5sinθ)
the equation of the ellipse is x216+y2b2=1 .........(2)
the equation of any tangent to the ellipse is y=mx+16m2+b2‾‾‾‾‾‾‾‾‾‾√ 
since it passes through the point P.
5sinθ=m.5cosθ+16m2+b2‾‾‾‾‾‾‾‾‾‾√5(sinθ−mcosθ)=16m2+b2‾‾‾‾‾‾‾‾‾‾√.........(3)

Answer 2

Answer:

±3/4

Step-by-step explanation:

4x^{2} -5x-1=0

4x^{2} -4x-x-1=0

4x(x-1)-1(x-1)=0

(4x-1) (x-1)=0

(4x-1)=0 and (x-1)=0

4x-1=0 and x-1=0

4x=1 and x=1

x=1/4 and x=1

α=1/4 and β=1 or α=1 and β=1/4

α-β=1/4-1 or α-β=1-1/4

α-β=1-4/4 or α-β=4-1/4

α-β=-3/4 or α-β=3/4

Step-by-step explanation: