Embibe Experts Solutions for Chapter: Two Dimensional Analytical Geometry-II, Exercise 1: Exercise

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Embibe Experts Mathematics Solutions for Exercise - Embibe Experts Solutions for Chapter: Two Dimensional Analytical Geometry-II, Exercise 1: Exercise

Attempt the free practice questions on Chapter 5: Two Dimensional Analytical Geometry-II, Exercise 1: Exercise with hints and solutions to strengthen your understanding. Mathematics Crash Course (Based on Revised Syllabus-2023) solutions are prepared by Experienced Embibe Experts.

Questions from Embibe Experts Solutions for Chapter: Two Dimensional Analytical Geometry-II, Exercise 1: Exercise with Hints & Solutions

MEDIUM
12th Tamil Nadu Board
IMPORTANT

Prove that the line 2x+y=1 is a tangent to the circle x2+y2+6x-4y+8=0.

EASY
12th Tamil Nadu Board
IMPORTANT

The equation of a circle of radius 6 units and whose centre lies on the negative direction of x-axis at a distance of 4 units from the origin is 

MEDIUM
12th Tamil Nadu Board
IMPORTANT

A focal chord of the ellipse x2a2+y2b2=1 makes an angle θ with major axis. Show that its length is 2ab2a2 sin2 θ+b2 cos2 θ.

HARD
12th Tamil Nadu Board
IMPORTANT

If PQ and QR are two focal chords of the ellipse x2a2+y2b2=1 and the eccentric angles of P, Q, R are respectively α, β, γ, show that tanα2, cotβ2, tanγ2 are in G.P..

MEDIUM
12th Tamil Nadu Board
IMPORTANT

Show that the tangent to a rectangular hyperbola terminated by its asymptotes is bisected at the point of contact.

HARD
12th Tamil Nadu Board
IMPORTANT

A cable of a suspension bridge is in the form of a parabola whose span is 40 metres. The road way is 5 metres below the lowest point of the cable. An extra support is provided across the cable 30 metres above the ground level. Find the length of the support if the height of the pillars are 55 metres.

HARD
12th Tamil Nadu Board
IMPORTANT

Find the equation and eccentricity of the ellipse, if the centre of ellipse is same as centre of the hyperbola 4x2-9y2+8x-36y-68=0, length of semi major axis is 3 units, length of minor axis is 2 units, the equation of major axis is x=-1.

HARD
12th Tamil Nadu Board
IMPORTANT

Find the centre, foci and vertices of the hyperbola 16x2-9y2-32x-18y+151=0 and draw the diagram.