Q. 35.0( 1 Vote )

# If the focu

Given the equation of directrix is x + y = 3 and focus is (- 2, 1). We know that the directrix and axis are perpendicular to each other. The axis also passes through the focus.

Let us find the slope of the directrix.

We know that the slope of the line ax + by + c = 0 is . m1 = - 1.

We know that the products of the slopes of the perpendicular lines (non - vertical) is - 1. Let us assume the slope of axis be m2.

m1.m2 = - 1

- 1.m2 = - 1

m2 = 1.

We know that the equation of the line passing through the point (x1, y1) and having slope m is (y - y1) = m(x - x1)

y - 1 = 1(x - (- 2))

y - 1 = x + 2

x - y + 3 = 0

On solving the lines x - y + 3 = 0 and x + y = 3, we get the intersection point to be (0, 3).

We know that vertex is the mid - point of focus and point of intersection of axis and directrix.

Let (x1, y1) be the vertex of the parabola.  (x1, y1) = (- 1, 2)

The correct option is C

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<span lang="EN-USRD Sharma - Mathematics

Which of thRD Sharma - Mathematics

The focus oRD Sharma - Mathematics

The length RD Sharma - Mathematics

The length RD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

If the coorRD Sharma - Mathematics

If the focuRD Sharma - Mathematics