Coordinate Geometry

14 solved problems from JEE previous year papers.

Straight Lines

Let A(α, β), B(1, 0), C(γ, δ) and D(1, 2) Be the Vertices of a Parallelogram ABCD With α, β, γ, δ ∈ Z. If AB = √10 and the Points A and C Lie on the Line 3y = 2x + 1, Then 2(α + β + γ + δ) Is Equal To

JEE Main 2024 PYQ: A(α,β), B(1,0), C(γ,δ), D(1,2) are vertices of a parallelogram. Find 2(α+β+γ+δ) using the diagonal-bisection…
Straight Lines

A Straight Line Cuts Off the Intercepts OA = a and OB = b on the Positive Directions of the x-axis and y-axis. If the Perpendicular From the Origin Makes an Angle π/6 With the Positive Direction of the y-axis and the Area of Triangle OAB Is 98√3/3, Then a² − b² Is Equal To

JEE Main 2023 PYQ: a line has intercepts OA=a, OB=b, with the perpendicular from the origin at angle π/6 to the y-axis and area…
Straight Lines

The Distance Between the Two Points A and A’ Which Lie on y = 2 Such That Both the Line Segments AB and A’B, Where B Is the Point (2, 3), Subtend an Angle π/4 at the Origin Is Equal To

JEE Main 2022 PYQ: A and A’ lie on y=2 such that segments AB and A’B (B=(2,3)) subtend angle π/4 at the origin. Find…
Circles

A Square Is Inscribed in the Circle x² + y² − 10x − 6y + 30 = 0. One Side of This Square Is Parallel to y = x + 3. If (xᵢ, yᵢ) Are the Vertices of the Square, Then the Sum of (xᵢ² + yᵢ²) Is Equal To

A square is inscribed in the circle x²+y²−10x−6y+30=0 with one side parallel to y=x+3. Find Σ(xᵢ²+yᵢ²) over the four vertices,…
Circles

A Line Segment AB of Length λ Moves Such That A and B Remain on the Periphery of a Circle of Radius λ. Then the Locus of the Point That Divides AB in the Ratio 2:3 Is a Circle of Radius

A line segment AB of length λ moves with both endpoints on a circle of radius λ. Find the radius of the locus of the point…
Circles

Let the Circle C₁: x² + y² − 2(x + y) + 1 = 0 and C₂ Be a Circle With Centre (−1, 0) and Radius 2. If the Common Chord of C₁ and C₂ Intersects the y-axis at P, Then the Square of the Distance of P From the Centre of C₁ Is

Circle C1: x²+y²−2(x+y)+1=0 and C2 have centre (−1,0), radius 2. Their common chord meets the y-axis at P. Find the square of the…
Circles

A Circle With Centre (2, 3) and Radius 4 Intersects the Line x + y = 3 at the Points P and Q. If the Tangents at P and Q Intersect at the Point S(α, β), Then 4α − 7β Is Equal To

A circle with centre (2,3) and radius 4 intersects x+y=3 at P and Q. Tangents at P, Q meet at S(α,β). Find 4α−7β using the chord…
Circles

If the Line ax + y = c Touches Both the Curves x² + y² = 1 and y² = 4√2x, Then |c| Is Equal To

Given the line ax+y=c is tangent to both the circle x²+y²=1 and the parabola y²=4√2x, find |c| by combining the circle’s…
Circles

The Equation of a Common Tangent to the Circle x² + y² − 6x = 0 and the Parabola y² = 4x Is

Find the equation of a common tangent to the circle x²+y²−6x=0 and the parabola y²=4x, by writing the parabola’s tangent in…
Circles

Let the Centre of a Circle C Be (α, β) and Its Radius r < 8. Let 3x + 4y = 24 and 3x − 4y = 32 Be Two Tangents and 4x + 3y = 1 Be a Normal to C. Then (α − β + r) Is Equal To

A circle with radius r
Straight Lines

Let the Straight Lines AB: x + y − 2 = 0 and AC: 3y − x = 2 Intersect the x-axis at B and C Respectively. If P Is the Orthocentre of Triangle ABC, Then the Area of Triangle CPB Is

Lines AB: x+y−2=0 and AC: 3y−x=2 meet the x-axis at B and C. Find the area of triangle CPB, where P is the orthocentre of…
Straight Lines

Distance of Origin From Centroid — Two Sides and Orthocenter Given

Given two sides of a triangle and its orthocenter, find the distance from the origin to the centroid by locating the altitudes…
Straight Lines

Triangle ABC: y=x Bisects ∠B, AC is 2x−y=2, 2AB=BC, A=(4,6) — Find α+2β

In triangle ABC, y=x bisects angle B, AC is 2x−y=2, and 2AB=BC. Given A=(4,6) and B=(α,β), find α+2β using the angle…
Straight Lines

A Line With Slope Greater Than One Passes Through the Point A(4, 3) and Intersects the Line x − y − 2 = 0 at the Point B. If the Length of AB Is √29/3, Then B Also Lies on the Line

A line through A(4,3) with slope greater than 1 meets x−y−2=0 at B, with AB=√29/3. Find which of four given lines B lies on.