What is an equation of a parabola with the given vertex (-2, 5) and focus (-2, 6)
Solution:
Given: Vertex of parabola (-2, 5) and focus (-2, 6)
As the vertex,(-2, 5)and focus (-2, 6) share same abscissa i.e. -2, parabola has axis of symmetry as x = -2 or x + 2 = 0
Hence, the equation of the parabola is of the type (y - k) = a(x - h)2
Where (h, k) is the vertex. Its focus then is (h, k + 1/4a).
As vertex is given to be (-2, 5), then the equation of parabola is y - 5 = a(x + 2)2
As the vertex is (-2, 5) and the parabola passes through the vertex and its focus is (-2, 5 + (1/4a) )
So, 1/4a = 6 ⇒ a = 24
and equation of parabola is y - 5 = 1/4(x + 2)2
⇒ 4y - 20 = (x + 2)2
= 4y - 20 = x2 + 4x + 4
⇒ 4y = x2 + 4x + 24
The equation of parabola is 4y = x2 + 4x + 24
What is an equation of a parabola with the given vertex (-2, 5) and focus (-2, 6)
Summary:
The equation of a parabola with the given vertex (-2, 5) and focus (-2, 6) is 4y = x2 + 4x + 24.
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