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Class 12
Math
Co-ordinate Geometry
Parabola
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521
150
IF y=mx+c touches the parabola
$y_{2}=4a(x+a)$
, then
521
150
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Related Questions
Suppose a parabola
$y=x_{2}−ax−1$
intersects the coordinate axes at three points A,B and C, respectively. The circumcircle of
$ΔABC$
intersects the y-axis again at the point
$D(0,t)$
. Then the value of t is
A tangent is drawn to parabola
$y_{2}=8x$
which makes angle
$θ$
with positive direction of x-axis. The equation of tangent is (A)
$y=xtanθ+2cotθ$
(B)
$ycotθ=x−2tanθ$
(C)
$ycotθ=x+2tanθ$
(D)
$ycotθ=x−tanθ$
$y_{2}=4x$
be the parabola and the points
$A(9,6),B(4,−4)$
lie on the parabola such that area of
$△ABC$
is maximum (given
$C$
lies at the arc contain origin). Find the maximum area of
$△ABC$
(A)
$2101 $
(B)
$269 $
(C)
$4125 $
(D)
$3521 $
Tangents are drawn to the parabola at three distinct points.
Prove that the orthocentre of the triangle formed by points of intersection of tangents always lies on the directrix.
Find the locus of midpoint of chord of the parabola
$y_{2}=4ax$
that passes through the point (3a,a).
Two mutually perpendicular tangents of the parabola
$y_{2}=4ax$
meet the axis at
$P_{1}andP_{2}$
. If S is the focal of the parabola, Then
$SP_{1}1 +SP_{2}1 $
is equal to
A set of parallel chords of the parabola
$y_{2}=4ax$
have their mid points on
Find the vertex, focus and directrix of the parabola
$x_{2}=2(2x+y)$
.
Related Questions
Suppose a parabola
$y=x_{2}−ax−1$
intersects the coordinate axes at three points A,B and C, respectively. The circumcircle of
$ΔABC$
intersects the y-axis again at the point
$D(0,t)$
. Then the value of t is
A tangent is drawn to parabola
$y_{2}=8x$
which makes angle
$θ$
with positive direction of x-axis. The equation of tangent is (A)
$y=xtanθ+2cotθ$
(B)
$ycotθ=x−2tanθ$
(C)
$ycotθ=x+2tanθ$
(D)
$ycotθ=x−tanθ$
$y_{2}=4x$
be the parabola and the points
$A(9,6),B(4,−4)$
lie on the parabola such that area of
$△ABC$
is maximum (given
$C$
lies at the arc contain origin). Find the maximum area of
$△ABC$
(A)
$2101 $
(B)
$269 $
(C)
$4125 $
(D)
$3521 $
Tangents are drawn to the parabola at three distinct points.
Prove that the orthocentre of the triangle formed by points of intersection of tangents always lies on the directrix.
Find the locus of midpoint of chord of the parabola
$y_{2}=4ax$
that passes through the point (3a,a).
Two mutually perpendicular tangents of the parabola
$y_{2}=4ax$
meet the axis at
$P_{1}andP_{2}$
. If S is the focal of the parabola, Then
$SP_{1}1 +SP_{2}1 $
is equal to
A set of parallel chords of the parabola
$y_{2}=4ax$
have their mid points on
Find the vertex, focus and directrix of the parabola
$x_{2}=2(2x+y)$
.
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