parabola comprehension (1 Viewer)

[juantheron]

A parabola is given. Also family of lines is given where are in Arithmetic Progression

The common point from which all the members of the given family of lines passes through is:

a) b) c) d) none

2. combined equation of embers of family of lines which are tangents to given parabola is:

a)

b)

c)

d)

3. Equation of chord of contact of above pair of tangents is:

a) b) c) d)

 

[braintic]

Question 1:

Since a, b, c form an AP:




So equation of line is:




Which is true independent of the values a and c when:

and

ie.


So the common point is (1, -4).

Question 2 is then a 2 unit question using the discriminant to find the 2 tangent equations in general form. Then multiply the two equations to get the final result.

Question 3 is a direction substitution into the chord of contact formula, except that the roles of x and y have been swapped in the formula.

 

[juantheron]

Thanks braintic