The focus of the parabola is (1,1) and the tangent at the vertex has the equation x+y=1 which of the following is correct

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Equation of parabola is x−y2=2x+y−1

Equation of parabola is x−y2=4x+y−1

The coordinates of the vertex 12,12

The length of the latursectum is 22

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The distance from focus to the tangent at vertex is a=2 Directrix is a line parallel to the tangent at vertex and at a distance of 22 units from focusDirectrix is passing through the image of focus in tangent at vertexHence the equation of the directrix is x+y=0By using the definition of the parabola, the locus is x+y22=x−12+y−12x2+y2+2xy=2x2+2y2−4x−4y+4=0x−y2=4x+y−1This is the equation of the parabolaVertex is the foot of the perpendicular of focus on the tangent at vertexhere vertex is 12,12a=12, hence the length of the latusrectum is 22

Watch 3-min video & get full concept clarity