Intersection Of A Circle And A Line
Gbogbo ọrọ náà
A straight line can slice through a circle at two points, just touch it at one, or miss it entirely. Which of these happens is decided by a single number from the quadratic you get when you combine their equations: the discriminant. This is coordinate geometry meeting the algebra of quadratics in a satisfying way.
In this lesson you will work with the equation of a circle \((x-a)^2+(y-b)^2=r^2\), substitute a line into it, and use the discriminant of the resulting quadratic to decide whether the line is a chord (two points), a tangent (one point) or misses the circle (none). One calculation settles the geometry.
Ebumnobi
- Know and use the equation of a circle with centre (a, b) and radius r.
- Solve problems involving the intersection of a circle and a straight line.
Nkuzi Olu
Gee ntị na nkuzi a na ngwa
Maapụ uche
E seela isiokwu a ka ị hụ otu echiche si ejikọta.
Mepee maapụ uche na ngwa
Kaadị ncheta
Omume ncheta ngwa ngwa n'ihe a na-anwale n'isiokwu a.
Mee omume kaadị ndị a na ngwa
Akwụkwọ Ọmụmụ
Ndetu Nkuzi Zuru Ezu di na Ngwa Green Bridge
Nweta ngwa Green Bridge CBT na ekwenti gi ma o bu kompiuta maka ulo akwukwo IGCSE zuru oke: akwukwo ule ndi gara aga, usoro nyocha, eserese uche, kaadi omumu na nkuzi olu.
Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Intersection Of A Circle And A Line. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- The equation of a circle with centre (a, b) and radius r is: A. (x - a)^2 + (y - b)^2 = r B. (x - a)^2 + (y - b)^2 = r^2 C. x^2 + y^2 = r D. (x + a)^2 + (y + b)^2 = r^2 Answer: B
- When a line is substituted into a circle, what does a discriminant of zero mean? A. The line is a chord B. The line is a tangent C. The line misses the circle D. The circle has no centre Answer: B
- For y = x + 1 and x^2 + y^2 = 25, the quadratic in x is x^2 + x - 12 = 0. Its discriminant is: A. -49 B. 1 C. 47 D. 49 Answer: D
- If the discriminant of the combined quadratic is negative, the line: A. Cuts the circle at two points B. Touches the circle C. Misses the circle D. Passes through the centre Answer: C
- A line cuts a circle at two points. The line is called a: A. Tangent B. Radius C. Chord D. Diameter Answer: C
Rue ajuju ndi a n'ime ngwa ahu
Rue ajuju ndi a n'ime ngwa ahu
Akwụkwọ A Na-atụ Aro
Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Intersection Of A Circle And A Line? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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