Master Conic Sections with Class 11 Maths JEE Brilliant Pala Notes. Gain in-depth insights, formulas, and problem-solving techniques to excel in JEE exams. Maximize your preparation with these SEO-optimized, comprehensive class notes for Conic Sections.
A conic is the locus of a point which keeps a constant ratio of the distance from a fixed point to the
distance from a fixed line
The fixed point is focus
The fixed line is directrix
SP
The fixed ratio e is called eccentricity
PM
If e 1 parabola
If e 1 ellipse
If e 1 hyperbola
Qn. Mind the equation of the conic whose focus is (2,–3) directrix is x y – 1 0 and having eccentricity
2
SP
Ans. Let P h, k be any point on the conic 2
PM
1
, 2 2
SP = h 2 k 3
h k 1
PM
2
SP e PM
2 2 h k 1
h 2 k 3 2
2
on squaring both sides
2 2 2
h 2 k 3 h k 1
h 2 4h 4 k 2 9 6k h 2 k 2 1 2hk 2k 2h
4h 6k 13 2hk 2k 2h 1
2h 8k 2hk 12 0
h 4k hk 6 0
h 4k hk 6 0
Putting h = x, k = y
Locus x 4y xy 6 0 (This is a hyperbola e 2 1.4 )
The line passing through the focus and perpendicular to the directrix is called axis
The point of intersection of the axis and the conic is called vertex
The chord of the conic passing through the focus are called focal chords
The chords r to the axis are called double ordinates.
Parabola
The focal chord which is also a double ordinate is called latus rectum
A parabola is the locus of a point which is equidistant from a fixed point called focus and a fixed line
called directrix. Thus from the vertex, distance to its focus and directrix are always equal. This distance
is represented as a
2
, Standard Parabolas
Case I
Equation y 2 4ax, a 0
vertex 0, 0
focus a, 0
directrix x a
Axis x axis y 0
Latus rectum, equation x a
length = 4a
focal distance (SP) = x+a
Case II
3
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