Length of Chord
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Q.
In the parabola y2=4 ax, the length of the chord passing through the vertex and inclined to the axis at π4 is
4√2a
2√2a
none of these
√2a
Q. If the x-intercept of the focal chord of the parabola y2−2y−4x+5=0 is 114, then find the length of chord.
- 152
- 252
- 254
- 154
Q. y2=4x and y2=−8(x−a) intersect at point A and C. Points O(0, 0), A, B(a, 0), C are concyclic.
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
- 48√3
- 96√2
- 36√6
- 54√5
Q.
Write the length of the chord of the parabola y2=4ax which passes through the vertex and is inclined to the axis π4.
Q. If the length of the chord of the parabola y2=4x whose slope is 1, is 10√2 units, then equation of the chord is
- x=y+21
- 4x=4y+21
- x=y−21
- 4y=4x+21
Q. Consider a circle S:(x+2)2+(y−8)2=16 and a parabola P:y2=8x.TA and TB are two tangents drawn from a point T on the parabola P=0 to the circle S=0 such that TA+TB is minimum. A and B are the points of contact.
List IList II(A)If T≡(a, b), then(a+b)equals(P)6(B)Sum of ordinates of A and B is(Q)8(C)Minimum value of (TA+TB) is (R)10(D)Area of ΔTAB is(S)12
Which of the following is a CORRECT combination ?
List IList II(A)If T≡(a, b), then(a+b)equals(P)6(B)Sum of ordinates of A and B is(Q)8(C)Minimum value of (TA+TB) is (R)10(D)Area of ΔTAB is(S)12
Which of the following is a CORRECT combination ?
- (C)→(S), (D)→(R)
- (C)→(R), (D)→(S)
- (C)→(P), (D)→(Q)
- (C)→(Q), (D)→(Q)
Q. If the length of the chord of the parabola y2=4x whose slope is 1, is 10√2 units, then equation of the chord is
- x=y+21
- 4x=4y+21
- x=y−21
- 4y=4x+21
Q. Let A and B be two distinct points on the parabola y2=4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be
- 2r
- −2r
- 1r
- −1r
Q. If the line y=mx+c is a common tangent to the hyperbola x2100−y264=1 and the circle x2+y2=36, then which one of the following is true?
- 4c2=369
- c2=369
- 8m+5=0
- 5m=4
Q. Let P(t1), Q(t2) be two points on the parabola y2=8x. Then which of the following is/are true?
- If the chord PQ meets the x−axis at (4, 0), then t1t2=−2
- If PQ is a focal chord, then t1t2=−2
- If t1=2, then the length of focal chord PQ is 254
- If t1=−12 and PQ meets the x−axis at (4, 0), then Q≡(32, 16)
Q.
Let L1 be a straight line passing through the origin and L2 be the straight line x + y=1. If the intercepts made by the circles x2+y2−x+3y=0 on L1 and L2 are equal then which of the following equations can represent L1?
- x+y=0
- x-7y=0
- 7x-y=0
- x-y=0
Q. The numbers of 3×3 matrices A whose entries are either 0 or 1 and for which the system A⎡⎢⎣xyz⎤⎥⎦=⎡⎢⎣100⎤⎥⎦ has exactly two distinct solutions is?
- 0
- 29−1
- 2
- 168
Q. If P(−3, 2) is one end of the focal chord PQ of the parabola y2+4x+4y=0, then the slope of the normal at Q is
- −12
- −2
- 12
- 2
Q. Consider the parabola whose focus at (0, 0) and tangent at vertex is x−y+1=0.
The length of chord of a parabola on the x−axis is
The length of chord of a parabola on the x−axis is
- 4√2
- 2√2
- 8√2
- 3√2
Q. If two normals to a parabola y2=4ax intersect at right angles, then the chord joining their feet passes through a fixed point whose co-ordinates are
- (2a, 0)
- (−2a, 0)
- (a, 0)
- none of these
Q. y2=4x and y2=−8(x−a) intersect at point A and C. Points O(0, 0), A, B(a, 0), C are concyclic.
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
- 96√2
- 48√3
- 54√5
- 36√6
Q. The area bounded by the tangent on the curve
y=4x2+2x at (0, 0) , y−10=−x and y=0 is
y=4x2+2x at (0, 0) , y−10=−x and y=0 is
- 1009 sq.units
- 20 sq.units
- 1003 sq.units
- 2009 sq.units
Q. Any chord AB of y62=4ax cuts the axis of the parabola at P, so that AP:AB=1:3 where A(at21, 2at1), B(at22, 2at2), then
- 2t1+t2=0
- t1+2t2=0
- t1t2=−4
- t1+t2=0
Q. y2=4x and y2=−8(x−a) intersect at point A and C. Points O(0, 0), A, B(a, 0), C are concyclic.
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
Tangents to parabola y2=4x at A and C intersect at point D and tangents to parabola y2=−8(x−a) intersect at point E, then the area of quadrilateral DAEC is
- 96√2
- 48√3
- 54√5
- 36√6
Q. Consider the parabola whose focus at (0, 0) and tangent at vertex is x−y+1=0.
The length of chord of a parabola on the x−axis is
The length of chord of a parabola on the x−axis is
- 4√2
- 2√2
- 8√2
- 3√2
Q. Consider a circle S:(x+2)2+(y−8)2=16 and a parabola P:y2=8x.TA and TB are two tangents drawn from a point T on the parabola P=0 to the circle S=0 such that TA+TB is minimum. A and B are the points of contact.
List IList II(A)If T≡(a, b), then(a+b)equals(P)6(B)Sum of ordinates of A and B is(Q)8(C)Minimum value of (TA+TB) is (R)10(D)Area of ΔTAB is(S)12
Which of the following is a CORRECT combination ?
List IList II(A)If T≡(a, b), then(a+b)equals(P)6(B)Sum of ordinates of A and B is(Q)8(C)Minimum value of (TA+TB) is (R)10(D)Area of ΔTAB is(S)12
Which of the following is a CORRECT combination ?
- (A)→(S), (B)→(R)
- (A)→(P), (B)→(S)
- (A)→(S), (B)→(P)
- (A)→(Q), (B)→(R)
Q. If a focal chord of the parabola y2=ax is 2x−y−8=0, then the equation of the directrix is
- x−4=0
- y+4=0
- y−4=0
- x+4=0