Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The common tangents to the circle x² + y² = a²/2 and the parabola y² = 4ax intersect at the focus of the parabola-

x² = 4ay
x² = –4ay
y² = –4ax
y² = 4a(x + a)

The correct answer is: y² = –4ax

Equation of a tangent to the parabola y² = 4ax is y = mx + a/m.
$fraction numerator a over denominator m end fraction equals open parentheses fraction numerator a over denominator square root of 2 end fraction close parentheses square root of 1 plus m to the power of 2 end exponent end root$ $rightwards double arrow$ 2 = m² (1 + m²)
$rightwards double arrow$ m⁴ + m² – 2 = 0 $rightwards double arrow$ (m² – 1) (m² + 2) = 0
$rightwards double arrow$ m² = 1 $rightwards double arrow$ x = ± 1
Hence the common tangents are y = x + a and y = –x –a which intersect at the point
(–a, 0) which is the focus of the parabola y² = –4ax.

Related Questions to study

If on a given base triangle b be described such that the sum of the tangents of the base angles is constant (k), then the locus of third vertex is -

If on a given base triangle b be described such that the sum of the tangents of the base angles is constant (k), then the locus of third vertex is -

Set of values of ‘h’ for which the number of distinct common normals of (x – 2)² = 4(y – 3) and x² + y² – 2x – hy – c = 0 (c > 0) is 3, is -

Set of values of ‘h’ for which the number of distinct common normals of (x – 2)² = 4(y – 3) and x² + y² – 2x – hy – c = 0 (c > 0) is 3, is -

PA and PB are the tangents drawn to y² = 4x from point P. These tangents meet the y-axis at the points A₁ and B₁ respectively. If the area of triangle PA₁ B₁ is 2 sq. units, then locus of ‘p’ is -

PA and PB are the tangents drawn to y² = 4x from point P. These tangents meet the y-axis at the points A₁ and B₁ respectively. If the area of triangle PA₁ B₁ is 2 sq. units, then locus of ‘p’ is -

parallel

If the chord of contact of tangents from a point P to the parabola y² = 4ax, touches the parabola x² = 4by, then the locus of P is a/an -

If the chord of contact of tangents from a point P to the parabola y² = 4ax, touches the parabola x² = 4by, then the locus of P is a/an -

AB, AC are tangents to a parabola y² = 4ax. If l₁, l₂, l₃ are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then -

AB, AC are tangents to a parabola y² = 4ax. If l₁, l₂, l₃ are the lengths of perpendiculars from A, B, C on any tangent to the parabola, then -

Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x² – 4x + 6y + 10 = 0, will touch a fixed line whose equation is -

Circle drawn having it’s diameter equal to focal distance of any point lying on the parabola x² – 4x + 6y + 10 = 0, will touch a fixed line whose equation is -

parallel

AB is a double ordinate of the parabola y² = 4ax. Tangents drawn to parabola at A and B meets y-axis at A₁ and B₁respectively. If the area of trapezium AA₁ B₁ B is equal to 12a², then angle subtended by A₁B₁ at the focus of the parabola is equal to -

AB is a double ordinate of the parabola y² = 4ax. Tangents drawn to parabola at A and B meets y-axis at A₁ and B₁respectively. If the area of trapezium AA₁ B₁ B is equal to 12a², then angle subtended by A₁B₁ at the focus of the parabola is equal to -

The parabola y² = 4x and the circle (x – 6)² + y² = r² will have no common tangent, if ‘r’ is equal to -

The parabola y² = 4x and the circle (x – 6)² + y² = r² will have no common tangent, if ‘r’ is equal to -

The name of the conic represented by the equation x² + y² – 2xy + 20x + 10 = 0 is-

The name of the conic represented by the equation x² + y² – 2xy + 20x + 10 = 0 is-

parallel

From an external point P tangents are drawn to the parabola y² = 4ax, then the equation to the locus of P when these tangents makes angles θ₁ and θ₂ with the axis, such that tan θ₁+ tan θ₂ with the axis, such that tan θ₁ + tan θ₂ is constant (= b), is -

From an external point P tangents are drawn to the parabola y² = 4ax, then the equation to the locus of P when these tangents makes angles θ₁ and θ₂ with the axis, such that tan θ₁+ tan θ₂ with the axis, such that tan θ₁ + tan θ₂ is constant (= b), is -

A point P (t², 2t) lies on the parabola y² = 4x, where FP is produced to B where F is focus. If PB = ƒ(t) and point B always lies on the line y – x = 2, then ƒ(t) is equal to-

A point P (t², 2t) lies on the parabola y² = 4x, where FP is produced to B where F is focus. If PB = ƒ(t) and point B always lies on the line y – x = 2, then ƒ(t) is equal to-

Equation of parabola having the extremities of it’s latus rectum as (3, 4) and (4, 3) is -

Equation of parabola having the extremities of it’s latus rectum as (3, 4) and (4, 3) is -

parallel

The set of pointS on the axis of the parabola y² = 4x + 8 from which the three normals to the parabola are all real and different is -

The set of pointS on the axis of the parabola y² = 4x + 8 from which the three normals to the parabola are all real and different is -

An equilateral triangle SAB is inscribed in the parabola y² = 4ax having it’s focus at ‘S’. If chord AB lies towards the left of S, then side length of this triangle is -

An equilateral triangle SAB is inscribed in the parabola y² = 4ax having it’s focus at ‘S’. If chord AB lies towards the left of S, then side length of this triangle is -

Binding energy per nucleon versas mass number curve for nuclei is shown in the fig W,X,Y and Z are four nuclei indicated on the curve The process that would release energy is

Binding energy per nucleon versas mass number curve for nuclei is shown in the fig W,X,Y and Z are four nuclei indicated on the curve The process that would release energy is

physics-General

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.