The line y = mx + c intersects the parabola la y^2= 4ax at the points P and Q.Show that the coordinates of the mid-point of PQ is ((2a-mc)/(m^2), (2a)/m) If the mid-point is M, find the locus of M whenm varies and c = 1

Jadon Melendez 2022-07-27 Answered
The line y = mx + c intersects theparabola y 2 = 4 a x at the points P and Q.Show that the coordinates of the mid-point of PQ is ( 2 a m c m 2 , 2 a m ).
If the mid-point is M, find the locus of M whenm varies and c = 1
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

losnonamern
Answered 2022-07-28 Author has 12 answers
y=mx+c eqn (1)
y 2 = a x eqn (2)
Square both side eqn 1
will get
y 2 = m 2 x 2 + 2 m c x + c 2 ... (3)
set 2 and 3 equals
4 a x = m 2 x 2 + 2 m c x + c 2
or
( m 2 ) x 2 + ( 2 m c 4 a ) x + ( c 2 ) = 0
x = b 2 a = ( 2 m c 4 a ) 2 m 2 = 2 a m c m 2
now plug in function 1
y = m ( 2 a m c m 2 ) + c = 2 a m c m + c m m = 2 a m
so we just showed that it works
( 2 a m c m 2 , 2 a m )
next,
when c=1:
( 2 a m m 2 , 2 a m )
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more