Question

y = 2x + C, 'c' being variable is a chord of the parabola y2 = 4x, meeting the parabola at A and
B. Locus of a point dividing the segment AB internally in the ratio 1:1 is :​

Answer 1

$\huge\boxed{\fcolorbox{violet}{violet}{Answer}}$

Parametric coordinates of parabola -

- wherein

For the parabola.

 

Selection formula -

- wherein

If P(x,y) divides the line joining A(x1,y1) and B(x2,y2) in ration 

 Parametric coordinates 

By section formula 

eliminating t, we get h2 = 2k

=> x2 = 2y

Option 1)

x2 = y 

This option is incorrect.

Option 2)

y2  =  x

This option is incorrect.

Option 3)

y2  =  2x

Answer 2

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

x = 15.65

y = 3.5

Step-by-step explanation:

Step 1

Find the equation for x and y

Equation for x is given as

x² = 7( 7+28) ..........Equation 1

14(14 + y) = x²........ Equation 2

Solving for Equation 1

x² = 7( 7+28)

x² = 7(35)

x² = 245

x = √245

x = 15.65

From Equation 1 , x² has been determined to be 245

Therefore we substitute 245 for y in Equation 2

14(14 + y) = x²........ Equation 2

14(14 + y) = 245

196 + 14y = 245

14y = 245 - 196

14y = 49

y = 49 ÷ 14

y = 3.5