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February 13, 2020

Coordinate Geometry - B.Stat. (Hons.) Admission Test 2005 – Objective Problem 5

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What are we learning ?

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Competency in Focus: Coordinate Geometry

This problem from B.Stat. (Hons.) based on coordinate geometry Admission Test 2005 – Objective Problem 5  is based nature of curve.

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First look at the knowledge graph:-

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Next understand the problem

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The equation $x(x+3)=y(y-1)-2$ represents
(A) a hyperbola

(B) a pair of straight lines
(C) a point

(D) none of the foregoing curves

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Coordinate Geometry

[/et_pb_accordion_item][et_pb_accordion_item title="Difficulty Level" _builder_version="4.1" open="off"]4/10[/et_pb_accordion_item][et_pb_accordion_item title="Suggested Book" _builder_version="4.3.1" open="off"]Challenges and Thrills in Pre College Mathematics

Excursion Of Mathematics[/et_pb_accordion_item][/et_pb_accordion][/et_pb_column][/et_pb_row][et_pb_row _builder_version="4.0"][et_pb_column type="4_4" _builder_version="3.25" custom_padding="|||" custom_padding__hover="|||"][et_pb_text _builder_version="4.0.9" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|0px|20px||" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3" inline_fonts="Aclonica"]

Start with hints 

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It cannot be a straight line because Straight line are linear equation of the form. \(ax+by+c=0\).

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So it may be a circle or a point if radius is zero, But when we generalized it to the standard form of circle we get negative radius. so it cant be either of this one.

Hint: Stanrd form of circle is $(x-h)^{2}+(y-k)^{2}=r^{2}$.

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Now lets try to factorize to find the product of two linear equations so as we can verify the pair of straight line.

$a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c=0$
This equation represents two straight lines, if $\Delta=a b c+2 f g h-a t^{2}-b g^{2}-c h^{2}=0$
or $\left|\begin{array}{lll}{a} & {h} & {g} \\ {h} & {b} & {f} \\ {g} & {f} & {c}\end{array}\right|=0$.

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Indian Statistical Institute and Chennai Mathematical Institute offer challenging bachelor’s program for gifted students. These courses are: B.Stat and B.Math program in I.S.I., B.Sc. Math in C.M.I.
The entrances to these programs are far more challenging than usual engineering entrances. Cheenta offers an intense, problem-driven program for these two entrances.

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