Question

an arch is in the form of a semi - ellips Determine
the height of the arch at a point and
ich the arch is tom wide and 4 m hight at the centre​

Answer 1

Answer:

Let equation of ellipse is in the form

x²/a² + y²/b² = 1 (a > b ) -----------(1)

Here width of an arch = 8 m = Length of major axis = 2a .e.g. 2a = 8 => a = 4

and night from centre = 2m = half of minor axis = 2b/2 = b .e.g. b = 2

now, put the values of a and b in equation(1)

x²/4² + y²/2² = 1

x²/16 + y²/4 = 1

See attachment ,

AP = 1.5 m

we see that , OP = 0A - AP

OP = 4 - 1.5 = 2.5 m

Let PQ = k

now, point Q ( 2.5 , k ) lies on equation of ellipse . hence, it will satisfy the equation of ellipse .

so, (2.5)²/16 + k²/4 = 1

6.25/16 + k²/4 = 1

k²/4 = 1 - 6.25/16 = 9.75/16

k² = 9.75/4

k = 1.56 ( approx )

Hence, height = 1.56 m

follow these method u will get ur answer