Question

find the equation of parabola whose focus is (1,1) and directrix is x+y+1=0

Answer 1

answer is here dear

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Answer 2

Thank you for asking this question. Here is your answer:

We have this equation:

x + y = 1

x + y = 1

y =  - x + 1

The slope of the tangent here is -1

And the slope of the line perpendicular to the tangent is 1

The line will pass through the focus y =  x + c which will pass through (1,1)

The equation for this would be: y = x

The point of intersection of x + y = 1 and x = y can be obtained by:

y + y = 1

2y = 1  

y = 1/2

The vertex for this is : (1/2, 1/2)

The distance between the focus and vertex is √[2x(1/2)²] = √2/2

The equation of parabola would be (y -1/2)² = (2x√2) x (x-1/2) y² + 1/4 - y = 2√2*x - √2

= 4y² - 4y - 8 x √2 *x + 4*√2 + 1 = 0

If there is any confusion please leave a comment below.