Find the points on the ellipse
5x² + y² = 5
that are farthest away from the point (1, 0).

9514 1400 393

  (-0.25, ±√4.6875)

Step-by-step explanation:

The square of the distance from a point on the ellipse to the point (1, 0) is ...

  d^2 = (x -1)^2 +y^2

Using the equation of the ellipse to write an expression for y^2, we have ...

  d^2 = (x -1)^2 +5 -5x^2

  d^2 = -4x^2 -2x +6

The expression on the right is that of a downward-opening parabola with ...

  a = -4, b = -2, c = 6

The maximum is located at ...

  x = -b/(2a) = -(-2)/(2(-4)) = -1/4

The value of y there is ...

  y^2 = 5 -5(-1/4)^2 = 4 11/16

  y = √4.6875

The points on the ellipse farthest from (1, 0) are (-0.25, ±√4.6875).

109 is the nearest whole number/final answer! : )

d

step-by-step explanation: