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Tangents of Parabola in Point Form, Tangents of Parabola in Slope Form is considered one of the most asked concept.
100 Questions around this concept.
If the line touches the parabola
, then the value of
is.
The slope of the line touching both the parabolas y2= 4x and x2 = -32y is:
Tangents are drawn to the parabola at the point
and
intersect at
. If '
' be the focus of the parabola then, SA, SC and SB forms
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Tangents of Parabola in Point Form
Note:
The same procedure can be applied to any general equation of parabola as well
For example, the tangent to 4y = x2 + 2x - 9 at (x1,y1) is 2(y+y1) = xx1 + (x+x1) - 9
Tangents of Parabola in Parametric Form
Proof:
Tangents of Parabola in Slope Form
If m is the slope of the tangent, then
The coordinates of point of contact are
Slope form of tangent for other forms of parabola
Note:
When the vertex of the shifted parabola at (h, k), then replace x by (x-h) and y by (y-k) in th equations of tangents
Point of Intersection of Tangent
Point of Intersection of tangents drawn at point P and Q is
TIP
The locus of the point of intersection of the mutually perpendicular tangents to a parabola is the directrix of the parabola.
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