Slope Form a Line
Trending Questions
Q. Find the coordinates of the foci, the vertices, the lenghts of major and minor axes and the eccentricity of the ellipse 9x2+4y2=36
Q. If a tangent to a parabola y2=4ax makes an angle of π3 with the axis of the parabola. Then point of contact(s) is/are
- (a3, −2a√3)
- (3a, −2√3a)
- (3a, 2√3a)
- (a3, 2a√3)
Q. If the ordinates of the points P and Q on the parabola y2=12x are in the ratio 1:2, then the locus of the point of intersection of normals to the parabola at P and Q is
- 343y2=12(x−6)3
- 343y2=12(x+6)3
- 343y2=−12(x−6)3
- 343y2=−12(x+6)3
Q. If from a point P, 3 normals are drawn, to parabola y2=4ax. Then the locus of P such that three normals intersect the x− axis at points whose distances from vertex are in A.P. is
- 27ay2=2(x+a)3
- 27ay2=2(x−a)3
- 27ay2=2(x+2a)3
- 27ay2=2(x−2a)3
Q. Let α, β are the angle of inclination of the tangents to the axis of the parabola y2=4ax drawn from the point P.
Match List I with the List II and select the correct answer using the code given below the lists :
List IList II (A)If cotαcotβ=k, then locus of P is (P)kx=a(B)If tanα+tanβ=k, then locus of P is(Q)y=k(x−a)(C)If tan(α+β)=k, then locus of P is(R)kx=y(D)If tanαtanβ=k, then locus of P is(S)xy=k(T)x=ka
Which of the following is the only CORRECT combination?
Match List I with the List II and select the correct answer using the code given below the lists :
List IList II (A)If cotαcotβ=k, then locus of P is (P)kx=a(B)If tanα+tanβ=k, then locus of P is(Q)y=k(x−a)(C)If tan(α+β)=k, then locus of P is(R)kx=y(D)If tanαtanβ=k, then locus of P is(S)xy=k(T)x=ka
Which of the following is the only CORRECT combination?
- (A)→(T), (B)→(R), (C→(Q), (D)→(P)
- (A)→(R), (B)→(Q), (C)→(P), (D)→(T)
- (A)→(P), (B)→(Q), (C)→(Q), (D)→(S)
- (A)→(S), (B)→(Q), (C)→(P), (D)→(T)
Q. If the line x+y−1=c touches the parabola x2+y−x=0, then the value of c is
Q. If normals are drawn from the point P whose slopes are m1 and m2. If m1⋅m2=α and point P lies on the parabola y2=4x, then the value of α is
Q. If from the vertex of the parabola y2=4ax pair of chords be drawn perpendicular to each other and with these chords as adjacent sides a rectangle is completed then the locus of the vertex of the farther angle of the rectangle is the parabola
- y2=4a(x−4a)
- y2=4a(x−6a)
- y2=4a(x−2a)
- y2=4a(x−8a)
Q.
When , what does equal?
Q. Let a line y=mx(m>0) intersect the parabola y2=x at a point P, other than the origin. The tangent to it at P meet the x− axis at point Q. If area △OPQ=4 sq.units, then 2m is equal to
Q. If from a point P, 3 normals are drawn, to parabola y2=4ax. Then the locus of P such that three normals intersect the x− axis at points whose distances from vertex are in A.P. is
- 27ay2=2(x+a)3
- 27ay2=2(x−a)3
- 27ay2=2(x+2a)3
- 27ay2=2(x−2a)3
Q. Normals are drawn from the point P with slopes m1⋅m2=α. If P lies on the parabola y2=4x itself, then α is equal to
Q. If a focal chord to y2=16x is tangent to (x−6)2+y2=2, then the possible value(s) of the slope of this chord is/are
- −1
- −1√2
- √2
- 1